Does Hebrews ever quote Jesus verbatim?

Hebrews 10:1-9 (DRB) For the law having a shadow of the good things to come, not the very image of the things; by the selfsame sacrifices which they offer continually every year, can never make the comers thereunto perfect: 2 For then they would have ceased to be offered: because the worshippers once cleansed should have no conscience of sin any longer: 3 But in them there is made a commemoration of sins every year. 4 For it is impossible that with the blood of oxen and goats sin should be taken away. 5 Wherefore when he cometh into the world, he saith: Sacrifice and oblation thou wouldest not: but a body thou hast fitted to me: 6 Holocausts¹ for sin did not please thee. 7 Then said I: Behold I come: in the head of the book it is written of me: that I should do thy will, O God. 8 In saying before, Sacrifices, and oblations, and holocausts for sin thou wouldest not, neither are they pleasing to thee, which are offered according to the law. 9 Then said I: Behold, I come to do thy will, O God: he taketh away the first, that he may establish that which followeth.

^{1 Archaic rendering meaning "whole burnt offering"}

St. Paul (almost unanimously the author according to the early Church, despite its being technically a unanimous Epistle) is not putting these words in the mouth of Jesus so much as He is relating the sentiment and mission of Jesus. Think of it as the metaphor of speech (where a metaphor says you are something, and this says you said something).

An analogy might be helpful.

Genesis 20:1-12 (DRB)

1 Abraham removed from thence to the south country, and dwelt between Cades and Sur, and sojourned in Gerara. 2 And he said of Sara his wife: She is my sister. So Abimelech the king of Gerara sent, and took her. 3 And God came to Abimelech in a dream by night, and he said to him: Lo thou shalt die for the woman thou hast taken: for she hath a husband. 4 Now Abimelech had not touched her, and he said: Lord, wilt thou slay a nation, that is ignorant and just? 5 Did not he say to me: She is my sister: and she say, He is my brother? in the simplicity of my heart, and cleanness of my hands have I done this. 6 And God said to him: And I know that thou didst it with a sincere heart: and therefore I withheld thee from sinning against me, and I suffered thee not to touch her. 7 Now therefore restore the man his wife, for he is a prophet: and he shall pray for thee, and thou shalt live: but if thou wilt not restore her, know that thou shalt surely die, thou and all that are thine. 8 And Abimelech forthwith rising up in the night, called all his servants: and spoke all these words in their hearing, and all the men were exceedingly afraid. 9 And Abimelech called also for Abraham, and said to him: What hast thou done to us? what have we offended thee in, that thou hast brought upon me and upon my kingdom a great sin? thou hast done to us what thou oughtest not to do. 10 And again he expostulated with him, and said, What sawest thou, that thou hast done this? 11 Abraham answered: I thought with myself, saying: Perhaps there is not the fear of God in this place: and they will kill me for the sake of my wife: 12 Howbeit, otherwise also she is truly my sister, the daughter of my father, and not the daughter of my mother, and I took her to wife.

Here, Abraham is quoted as having spoken (the Hebrew literally says, "and Abraham said, 'For I said,...'") the words, "Perhaps there is not the fear of God in this place: and they will kill me for the sake of my wife," although these words merely capture Abraham's thoughts, and are not a literal quotation of what Abraham actually spoke.

In a similar way, Psalms and other passages of Scripture can be put in the mouth of Jesus, not as a literal quote, but as pointing out that Jesus best fulfills the Scripture referenced (exceptions are of course instances where the narrative indicates, being a history of events, that He uttered certain words or quoted certain Scriptures).

Thus, Hebrews is saying that Jesus' mission and life can be summed up in the words, "Sacrifice and oblation did not please thee, but a body thou hast prepared for me," because Jesus came to be the end of sacrifices, being the ultimate Sacrifice.

Does St. Paul ever quote Jesus?

I personally know of of only two instances where St. Paul quotes Jesus directly, having been taught it by Tradition:

Acts 20:35 (DRB) I have shewed you all things, how that so labouring you ought to support the weak, and to remember the word of the Lord Jesus, how he said: It is a more blessed thing to give, rather than to receive.

1 Corinthians 11:22-25 (DRB) What, have you not houses to eat and to drink in? Or despise ye the church of God; and put them to shame that have not? What shall I say to you? Do I praise you? In this I praise you not. 23 For I have received of the Lord that which also I delivered unto you, that the Lord Jesus, the same night in which he was betrayed, took bread. 24 And giving thanks, broke, and said: Take ye, and eat: this is my body, which shall be delivered for you: this do for the commemoration of me. 25 In like manner also the chalice, after he had supped, saying: This chalice is the new testament in my blood: this do ye, as often as you shall drink, for the commemoration of me.

There are of course probably too many instances too enumerate where St. Paul alludes directly or indirectly to the words and teaching of Jesus, but that is not direct quotation.

However, to suppose that what we have in the New Testament comes close to capturing the majority of the teaching of St. Paul and the other Apostles contradicts basic common sense: the content of the Epistles themselves assume that teaching had already taken place and that they merely supplement and correct errors and build up faith—they are not the first or last time St. Paul teaches to the churches, nor the only churches he taught. Moreover, the most ancient liturgies, as evidenced in the apostolic fathers, indicate that reading the words and sayings of Jesus in the Gospels and Epistles was normative for the liturgy of the Eucharist, and thus before this point, 2 Timothy 2:2's core modus operandi would have been in force to the effect that those who heard Jesus would have related his words to the first bishops and their successors, even before the Epistles and Gospels, in order for them to be taught if not read from each week.