In the New Testament, Jesus never prescribes or approves of any particular canon
Jesus doesn't anywhere speak of the canon,1 except to refer to common ways of dividing them: "the Law and the Prophets" (Matthew 5:17), "the Law, the Prophets, and the Psalms" (Luke 24:44; cf. 24:27). This latter one is significant for our purpose becaues among the Jews, the Psalms began the section of Scriptures known as the Writings.
Yet even in the fifth century or sixth century we read Rabbis quoting from Sirach as Scripture (part of the Writings, using the formula, "as it is written"):2
Baba Kamma, 92b
א"ל רבא לרבה בר מרי מנא הא מילתא דאמרי אינשי מטייל ואזיל דיקלא בישא גבי קינא דשרכי אמר ליה דבר זה כתוב בתורה שנוי בנביאים ומשולש בכתובים ותנן במתניתין ותנינא בברייתא
כתוב בתורה דכתיב וילך עשו אל ישמעאל שנוי בנביאים דכתיב ויתלקטו אל יפתח אנשים רקים ויהיו עמו ומשולש בכתובים דכתיב כל עוף למינו ישכון ובני אדם לדומה לו
Raba said to Rabbah bar Mari: Whence do people derive the saying: A bad palm tree wanders about seeking a grove of barren trees? Who said to him: This is written in the Torah, and repeated in the Prophets, and is repeated again in the Writings, and we learned it as well from an oral tradition, and from yet an extra source of tradition. It is written in the Law, as it is written: And so Esau went to Ishmael [Genesis 28]. It is repeated in the Prophets [Judges 11], as it is written: And some foolish men gathered themselves around Jephthah, and they went with him. And is repeated again in the Writings, as it is written: All fowl will resort unto their kind, and a man unto another like to himself. [Sirach 13, 27].
Mishnah Yadayim also speaks about what renders the hands ritually unclean (i.e. what is Holy Scripture in this case).
Mishnah Yadayim, 3:5
רַבִּי יְהוּדָה אוֹמֵר ... כל כתבי הקדשׁ מטמאין את הידים. שׁיר השׁירים וקהלת מטמאין את הידים. רבי יהודה אומר, שׁיר השׁירים מטמא את הידים, וקהלת מחלקת. רבי יוסי אומר, קהלת אינו מטמא את הידים ושׁיר השׁירים מחלקת. רבי שׁמעון אומר, קהלת מקלי בית שׁמאי ומחמרי בית הלל. אמר רבי שׁמעון בן עזאי, מקבל אני מפי שׁבעים ושׁנים זקן, ביום שׁהושׁיבו את רבי אלעזר בן עזריה בישׁיבה, שׁשׁיר השׁירים וקהלת מטמאים את הידים. אמר רבי עקיבא, חס ושׁלום, לא נחלק אדם מישׂראל על שׁיר השׁירים שׁלא תטמא את הידים, שׁאין כל העולם כלו כדאי כיום שׁנתן בו שׁיר השׁירים לישׂראל, שׁכל הכתובים קדשׁ, ושׁיר השׁירים קדשׁ קדשׁים. ואם נחלקו, לא נחלקו אלא על קהלת. אמר רבי יוחנן בן יהושׁע בן חמיו שׁל רבי עקיבא, כדברי בן עזאי, כך נחלקו וכך גמרו
... Rabbi Judah says ... All the Holy Scriptures render the hands unclean. Song of Songs renders the hands unclean. Rabbi Judah says that Song of Songs and Ecclesiastes render the hands unclean, but about Ecclesiastes there is dispute. Rabbi Josei says Ecclesiastes does not render the hands unclean, but about Song of Songs there is dispute. Rabbi Simon says that with regard to Ecclesiastes the school of Shamai is more lenient, and the house of Hillel more strict. Rabbi Simon ben Azzai said: I received a tradition from the seventy-two elders on the day they appointed Eleazar ben Azariah over the college that Ecclesiastes and Song of Songs render the hands unclean. Rabbi Akiba said: Far be it! No man of Israel has ever disputed that Song of Songs renders the hands unclean. For the whole world is not as worthy as the day on which Song of songs was given to Israel: all the Books are holy, but the Song of Songs the Holy of Holies; if there was ever a dispute, it was about Ecclesiastes. Rabbi John ben Joshua, son of Rabbi Akiba's father in law, said in accordance with words of ben Azzai: so they disputed, and so they reached a decision.
There was clearly no consensus even in the second century, or this dispute would never have taken place in the first place.
There is also attestation to the fact that the primitive church at least regarded Sirach other later books as Holy Scripture, by inference from the following (again second century):
Tosefta Yadayim, 2
הגליונים ספרי מינין אינן מטמאות הידים. ספרי בן סירא וכל הספרים שנכתבו מכאן ואילך אינן מטמאין את הידים
... The the Gospels of the Christians4 do not render the hands unclean: nor does, henceforth, Sirach, or any of the books written after it.
This is as ridiculous and irrelevant as saying, "The Gospels and Spiderman comics aren't Holy Scripture" unless Sirach and the later books of the 'apocrypha' (a question-begging term for these books) were considered Holy Scripture at least by second century Christians.3
Moreover, Palestinian Jews are not the only Jews. The diaspora Jews clearly seem to have at the least revered the deuterocanonical books as doctrinally sound, and possibly (likely) viewed them as Scripture, found in the various codices of the Septuagint. Indeed, that most of the deuterocanonical books have been discovered to have Hebrew or Aramaic originals, proves they were specifically Jewish sacred works, not the inventions of Christian after Jesus, or by the Church.
Argument from Silence Useless
An argument of silence, such as "Jesus never quotes from these books" won't work, as He doesn't quote from Judges, Ruth, Ezra, Esther, Ecclesiastes, Song of Solomon, Lamentations, Obadiah, Jonah, Zephaniah, nor do any of the apostles or writers of the New Testament. (But of course it's already a fallacious argument without begging the question as to whether these books are obviously to be considered part of the Bible.)
Likely Allusions in the New Testament
Although Jesus doesn't speak to the canon, we can derive some sense of how the apostles and other writers of the New Testament viewed these books, whom we can safely assume agreed with Jesus.
A striking example of a clear allusion to a book is in Revelation, where St. John describes seeing "the seven angels who stand before God," and that they offer our prayers before God. However, this comes from the book of Tobit (Aramaized verision of the Hebrew name Tobiyah, meaning "God's goodness"), which by implication is proved to have inspired knowledge of the heavenly realm.
Aramaic Tobit, Vul 12:12-15
... I offered thy prayer to the Lord. And because thou wast acceptable to God, it was necessary that trial should prove thee. And now the Lord hath sent me to heal thee, and to deliver Sara thy son's wife from the devil. For I am the angel Raphael,5 one of the seven who stand before the Lord.
And when he opened the seventh seal, there was silence in heaven for about a half an hour. And I saw the seven angels who stand before God, and trumpets were given to them. And behold another angel came and stood at the altar, having a golden censer, and much incense was given to him, that he should offer the prayers of all the saints at the golden altar which is before the throne. And the smoke of the incense of the prayers of the saints ascended from the hand of the angel before God.
Another example is St. Paul alluding to the book of Wisdom (also called Wisdom of Solomon) in several Epistles.
If St. Paul quotes or alludes to a certain passage, he expects his readers are aware of the immediate context of that passage. This is the same here, Wisdom surpasses even the stars, is is the effulgence of God's very glory, and thus his primary and preliminary argument in Hebrews that Christ, the "wisdom of God" (1 Cor. 1:24) is superior to the angels, reminds him of this passage of Scripture:
For wisdom is more active than all active things: and reacheth everywhere by reason of her purity. For she is a vapour of the power of God, and a certain pure emanation of the glory of the almighty God: and therefore no defiled thing cometh into her. For she is the effulgence of eternal light, and the unspotted mirror of God's majesty, and the image of his goodness. And being but one, she can do all things: and remaining in herself the same, she reneweth all things, and through nations conveyeth herself into holy souls, she maketh the friends of God and prophets. For God loveth none but him that dwelleth with wisdom. For she is more beautiful than the sun, and above all the order of the stars: being compared with the light, she is found before it. For after this cometh night, but no evil can overcome wisdom.
God, who, at sundry times and in divers manners, spoke in times past to the fathers by the prophets, last of all, in these days hath spoken to us by his Son, whom he hath appointed heir of all things, by whom also he made the world. Who being the effulgence of his glory, and the express image of his substance, and upholding all things by the word of his power, making purgation of sins, sitteth on the right hand of the majesty on high. Being made so much better than the angels, as he hath inherited a more excellent name than they.
Also, the word used for "effulgence" (απαυγασμα—radiance, effulgence) used in both is an extremely rare word in Greek literature, and is only used here in Hebrews 1 and Wisdom 7 in the entire Greek Bible—further excluding all doubt as to the allusion here intended; it comes close to a quote.
Wisdom 13:1-9; 14:22-31 1 But all men are vain, in whom there is not the knowledge of God: and who by these good things that are seen, could not understand him that is, neither by attending to the works have acknowledged who was the workman: 2 But have imagined either the fire, or the wind, or the swift air, or the circle of the stars, or the great water, or the sun and moon, to be the gods that rule the world. 3 With whose beauty, if they, being delighted, took them to be gods: let them know how much the Lord of them is more beautiful than they: for the first author of beauty made all those things. 4 Or if they admired their power and their effects, let them understand by them, that he that made them, is mightier than they: 5 For by the greatness of the beauty, and of the creature, the creator of them may be seen, so as to be known thereby. 6 But yet as to these they are less to be blamed. For they perhaps err, seeking God, and desirous to find him. 7 For being conversant among his works, they search: and they are persuaded that the things are good which are seen. 8 But then again they are not to be pardoned. 9 For if they were able to know so much as to make a judgment of the world: how did they not more easily find out the Lord thereof? ... And it was not enough for them to err about the knowledge of God, but whereas they lived in a great war of ignorance, they call so many and so great evils peace. 23 For either they sacrifice their own children, or use hidden sacrifices, or keep watches full of madness, 24 So that now they neither keep life, nor marriage undefiled, but one killeth another through envy, or grieveth him by adultery: 25 And all things are mingled together, blood, murder, theft and dissimulation, corruption and unfaithfulness, tumults and perjury, disquieting of the good, 26 Forgetfulness of God, defiling of souls, changing of nature, disorder in marriage, and the irregularity of adultery and uncleaness. 27 For the worship of abominable idols is the cause, and the beginning and end of all evil. 28 For either they are mad when they are merry: or they prophesy lies, or they live unjustly, or easily forswear themselves. 29 For whilst they trust in idols, which are without life, though they swear amiss, they look not to be hurt. 30 But for two things they shall be justly punished, because they have thought not well of God, giving heed to idols, and have sworn unjustly, in guile despising justice. 31 For it is not the power of them, by whom they swear, but the just vengeance of sinners always punisheth the transgression of the unjust.
Romans 1:18-32 For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of those men that detain the truth of God in injustice: because that which is known of God is manifest in them. For God hath manifested it unto them. For the invisible things of him, from the creation of the world, are clearly seen, being understood by the things that are made; his eternal power also, and divinity: so that they are inexcusable. Because that, when they knew God, they have not glorified him as God, or given thanks; but became vain in their thoughts, and their foolish heart was darkened. For professing themselves to be wise, they became fools. And they changed the glory of the incorruptible God into the likeness of the image of a corruptible man, and of birds, and of fourfooted beasts, and of creeping things. Wherefore God gave them up to the desires of their heart, unto uncleanness, to dishonour their own bodies among themselves. Who changed the truth of God into a lie; and worshipped and served the creature rather than the Creator, who is blessed for ever. Amen. For this cause God delivered them up to shameful affections. For their women have changed the natural use into that use which is against nature. And, in like manner, the men also, leaving the natural use of the women, have burned in their lusts one towards another, men with men working that which is filthy, and receiving in themselves the recompense which was due to their error. And as they liked not to have God in their knowledge, God delivered them up to a reprobate sense, to do those things which are not convenient; Being filled with all iniquity, malice, fornication, avarice, wickedness, full of envy, murder, contention, deceit, malignity, whisperers, detractors, hateful to God, contumelious, proud, haughty, inventors of evil things, disobedient to parents, foolish, dissolute, without affection, without fidelity, without mercy. Who, having known the rightousness of God, did not understand that they who do such things, are worthy of death; and not only they that do them, but they also that consent to them that do them.
Jesus seems to make profuse use of Sirach (perhaps explaining Tosefta Yadayim cited above):
Sirach 7:15 Be not full of words in a multitude of ancients, and repeat not the word in thy prayer.
Matthew 6:7 And when you are praying, do not babble at length, as the heathens. For they think that in their much speaking they may be heard.
Sirach 28:2 Forgive thy neighbour if he hath hurt thee: and then shall thy sins be forgiven to thee when thou prayest.
Matthew 6:14 For if you will forgive men their offences, your heavenly Father will forgive you also your offences.
Sirach 51:33-36 I have opened my mouth, and have spoken: buy her for yourselves without silver, and submit your neck to the yoke, and let your soul receive discipline: for she is near at hand to be found. Behold with your eyes how I have laboured a little, and have found much rest to myself. Receive ye discipline as a great sum of money, and possess abundance of gold by her.
Revelation 3:18-20 I counsel thee to buy of me gold fire tried, that thou mayest be made rich; and mayest be clothed in white garments, and that the shame of thy nakedness may not appear; and anoint thy eyes with eyesalve, that thou mayest see. 19 Such as I love, I rebuke and chastise. Be zealous therefore, and do penance. 20 Behold, I stand at the gate, and knock. If any man shall hear my voice, and open to me the door, I will come in to him, and will sup with him, and he with me.
Matthew 11:28-30 Come to me, all you that labour, and are burdened, and I will refresh you. Take up my yoke upon you, and learn of me, because I am meek, and humble of heart: and you shall find rest to your souls. For my yoke is sweet and my burden light.
Sirach 4:12 Wisdom inspireth life into her children, and protecteth them that seek after her, and will go before them in the way of righteousness.
Luke 7:35 And wisdom is justified in all her children.
Sirach 7:19 Humble thy spirit very much: for the vengeance on the flesh of the ungodly is fire and worms.
Judith 16:20-21 Woe be to the nation that riseth up against my people: for the Lord almighty will take revenge on them, in the day of judgment he will visit them. 21 For he will give fire, and worms into their flesh, that they may burn, and may feel for ever.
Mark 9:41-47 And whosoever shall scandalize one of these little ones that believe in me; it were better for him that a millstone were hanged around his neck, and he were cast into the sea. 42 And if thy hand scandalize thee, cut it off: it is better for thee to enter into life, maimed, than having two hands to go into hell, into unquenchable fire: 43 Where their worm dieth not, and the fire is not extinguished. 44 And if thy foot scandalize thee, cut it off. It is better for thee to enter lame into life everlasting, than having two feet, to be cast into the hell of unquenchable fire: 45 Where their worm dieth not, and the fire is not extinguished. 46 And if thy eye scandalize thee, pluck it out. It is better for thee with one eye to enter into the kingdom of God, than having two eyes to be cast into the hell of fire: 47 Where their worm dieth not, and the fire is not extinguished.
And countless other possible allusions and linguistic borrowings.
At the least, Jesus and the authors of the New Testament appear to have approved of these books. I would argue they cite them in a way that impies they have authority (think Paul assuming the greater context of a passage he quotes a little of conhesively proves his point, not that they 'happened to be right,' especially with Tobit.
Moreover, many prophetic sayings are found in these books, such as Wisdom:
Wisdom 9:19 For by Wisdom they were healed, whosoever have pleased thee, O Lord, from the beginning.
The exclusive and sole reason any man was spared since the Fall was because of Christ.
Wisdom 14:7 For blessed is the wood by which righteousness cometh.
For they have said, reasoning with themselves, but not right: The time of our life is short and tedious, and in the end of a man there is no remedy, and no man hath been known to have returned from hell: 2 For we are born of nothing, and after this we shall be as if we had not been: for the breath in our nostrils is smoke: and speech a spark to move our heart, 3 Which being put out, our body shall be ashes, and our spirit shall be poured abroad as soft air, and our life shall pass away as the trace of a cloud, and shall be dispersed as a mist, which is driven away by the beams of the sun, and overpowered with the heat thereof: 4 And our name in time shall be forgotten, and no man shall have any remembrance of our works. 5 For our time is as the passing of a shadow, and there is no going back of our end: for it is fast sealed, and no man returneth. 6 Come therefore, and let us enjoy the good things that are present, and let us speedily use the creatures as in youth. 7 Let us fill ourselves with costly wine, and ointments: and let not the flower of the time pass by us. 8 Let us crown ourselves with roses, before they be withered: let no meadow escape our riot. 9 Let none of us go without his part in luxury: let us everywhere leave tokens of joy: for this is our portion, and this our lot. 10 Let us oppress the poor just man, and not spare the widow, nor honour the ancient grey hairs of the aged. 11 But let our strength be the law of justice: for that which is feeble, is found to be nothing worth. 12 Let us therefore lie in wait for the just, because he is not for our turn, and he is contrary to our doings, and upbraideth us with transgressions of the law, and divulgeth against us the sins of our way of life. 13 He boasteth that he hath the knowledge of God, and calleth himself the son of God. 14 He is become a censurer of our thoughts. 15 He is grievous unto us, even to behold: for his life is not like other men's, and his ways are very different. 16 We are esteemed by him as triflers, and he abstaineth from our ways as from filthiness, and he preferreth the latter end of the just, and glorieth that he hath God for his father. 17 Let us see then if his words be true, and let us prove what shall happen to him, and we shall know what his end shall be. 18 For if he be the true son of God, he will defend him, and will deliver him from the hands of his enemies. 19 Let us examine him by outrages and tortures, that we may know his meekness and try his patience. 20 Let us condemn him to a most shameful death: for there shall be respect had unto him by his words. 21 These things they thought, and were deceived: for their own malice blinded them. 22 And they knew not the secrets of God, nor hoped for the wages of justice, nor esteemed the honour of holy souls. 23 For God created man incorruptible, and to the image of his own likeness he made him. 24 But by the envy of the devil, death came into the world: 25 And they follow him that are of his side.
The conspiracy against Christ.
(Wis. 2:20 | Jas. 5:6; Wis. 2:3 | Jas. 4:14; Wis. 2:12,20 | Acts 7:51-53; Wis. 2:12 | Mt. 23/Jn.7:19; Wis. 2:15-16 | Jn. 7:46/Mt. 23:27-28/Jn. 5:18; Wis. 2:16 | Mt. 5:2-10; Wis. 2:17-18 | Mt. 27:41-43. Wis. 2:19 (cf. Jas. 5:6) | Jn. 11:46-48, 53; 19:1/ Mt. 26:67/ Lk. 24:20)
The canon is not clearly outlined in Scripture itself (and to seek it therein is to already assume, not prove, a canon), and any 'it seems to be the Word of God' or 'it seems not to be the Word of God' argument is inherently subjective, and presupposes a canon of works on which to base such a judgement. Therefore, the canon is something settled by an authority higher than mere subjective feeling—but not by post-Christian Rabbis who rise no higher than such. According to the ancient Church, the Church settled the canon, with its inherent power to bind and loose matters upon the faithful, and when it did meet to settled the issue of canon, it settled upon the Catholic canon of the Bible.6
Thus, at best, the notion that Jews or Jesus rejected these books before the Rabbis of the second century and beyond is unfounded, and based on no evidence from history. At best, one has to trust the "decision" made by the Rabbis in the second century on what is Scripture or not, in order to condemn these books found in the Dead Sea Scrolls, the Septuagint, and moreover the Ethiopian Jews' canon.
1 In Luke 11:51/Matthew 23:35, often cited by Protestants, Jesus is not talking about inspiration or the extent of the canon, but the prophets who were murdered by their own people. It's more likely He is picking examples of righteous men speaking the truth, and for that reason being murdered, which He identifies Himself with (Jn. 7:19; cf. Mt. 21:37-38). Moreover, at best, one would have to demand we see "Zechariah son of Barachiah" as the same person as the Zechariah mentioned in the Old Testament, "Zechariah son of . Cf. Eph. 4:11; 2 Pet. 3:15-16; Rev. 22:18.
2 Composed in Talmudic Babylon, 450-550 A.D.
3 It's not necessary to cite early Christian usage of these books, since it's so ubiquitous and known already.
4 The Jewish Rabbis of the Talmudic era were wont to call Gospel books even gilyon ("Perverse Scroll") or avon gilyon ("Iniquitous Scroll"), both plays on the Greek word for gospel, euangelion. (Shabbat 116a)
5 Raphael is Hebrew for "Healing of God" It could also have said, "I am the angel of God's healing." Proves the Hebrew origin of the work.
6 E.g. St. Jerome is epitomic, "For the studies of the Hebrews rebuke us and find fault with us, to translate this [book of Tobit] for the ears of Latins contrary to their canon. But it is better to be judging the opinion of the Pharisees to displease and to be subject to the commands of bishops." (Preface to Tobit). "this book is found by the Council of Nicaea to have been counted among the number of the Sacred Scriptures" (Preface to Judith). The local Councils of Hippo, Rome, and Carthage, in the fourth century, and Ecumenical Councils of Nicaea II, Florence (with which the Eastern Orthodox agreed for a brief period) and the Council of Trent in the middle ages, all confirm the same canon of the Old Testament.