What is the biblical basis for Jeremiah and John the Baptist being born without original sin?
The answer is Ephesians1:4-6, because both prophet Jeremiah & St.John the Baptist are chosen before the foundation of the world.The keyword is "holy & blameless".
IMPORTANT NOTE TO PONDER :
God put the WORD/Logos into Jeremiah's mouth, while St.John the Baptist in the womb of her mother St.Elizabeth was visited by "the Theotokos who is bearing the Logos/Incarnate WORD in Her most pure womb."
Ephesians 1:4-6 New International Version (NIV)
"For he chose us in him before the creation of the world to be holy and blameless in his sight. In love he predestined us for adoption to sonship through Jesus Christ, in accordance with his pleasure and will to the praise of his glorious grace, which he has freely given us in the One he loves.
What is the next good question? Why is St.John the Baptist nativity was celebrated by Church Liturgical calendar along with Jesus & Mary while prophet Jeremiah was not included?
Of all the feast days in the liturgical calendar of the Catholic Church, only three birthdays are observed: the Nativity of our Divine Savior, Who is Holiness Itself; St. John the Baptist, who was sanctified in his mother's womb; and Mary, the ever-virgin Mother of God, whose birthday is celebrated on the eighth of September.http://www.thesacredheart.com/mary.htm
If St.John the Baptist nativity was celebrated alongside Jesus & Mary it would be logical to think that he was also born like Jesus & Mary free from original sin and the most important thing is St.John the Baptist was cleansed from all stain of original sin too. Now, how can the Church explain this feast of nativity of St.John the Baptist?
Let us be clear on the proper understanding on this, St.John the Baptist contracted the guilt of original sin that was passed on by his father Zechariah. The seed that comes from Zechariah was not spotless if we compare it to the "spotless seed" that was poured out by St.Joachim the pious father of the Blessed Virgin Mary.
“O most blessed loins of Joachim from which came forth a spotless seed! O glorious womb of Anne in which a most holy offspring grew.” John of Damascus, Homily I (ante A.D. 749).
"O blessed loins of Joachim, whence the all-pure seed was poured out! O glorious womb of Anna, in which the most holy fetus grew and was formed, silently increasing! O womb in which was conceived the living heaven, wider than the wideness of the heavens."
A Little Treatise on Mary by St. John Damascene
For a more fuller explanation on "spotless seed" of St. Joachim please see this link.
Did St. Joachim prevent the transmission of original sin to Mary by overcoming concupiscence?
If we based our appreciation on the Church Liturgical Feast celebration of St.John the Baptist nativity over prophet Jeremiah nativity it would seem that Jeremiah was born cleansed of original sin but with the stain of original sin not fully wash away. How come? What is the biblical explanation of this mystery?
The Sacrament of Baptism washes away our soul of original sin and the sanctifying grace was poured out. But since we are all descendant of Adam, our soul live in our body with a fallen nature meaning we come from a "corrupted seed". Our bodies having inherited a fallen nature had an inclination to sin or what we called "concupiscence". The Sacrament of Baptism does not wash away the "concupiscence". The Catholic Church teaches that thru continuous worthy reception of the Holy Eucharist the "concupiscence" are wash-away and the "transformation" process will take effect. CCC1000 is the Church Teaching on the washing away of the "concupiscence" meaning our fallen nature can be healed if we received the "body,blood, soul & divinity" of our Lord Jesus Christ in the Holy Eucharist.
For a complete explanation on the "washing away" of the concupiscence" please see this link; How can a Christian be freed from concupiscence and thereby possess a sinless body?
Prophet Jeremiah and St.John the Baptist were both "sanctified" in the womb. But what makes St.John the Baptist nativity greater than prophet Jeremiah was their Mother participation in embracing God's Will or purpose for their child. The bible does not state any significance attributes for the Mother of Jeremiah, while St.John the Baptist mother was mentioned particularly as "filled with the Holy Spirit". Let's ponder the beautiful mystery of why St.John the Baptist was healed of "concupiscence" while still in her mother's womb. The secret, is how the Theotokos for three months taught St.Elizabeth the prayer of consecration by daily praying the Magnificat as revealed by Blessed Catherine Emmerich. Not only the praying of Magnificat but especially St.Elizabeth must be fed mystically too by the "Bread of Life".
More on the Blessed Virgin Mary "Mystery of Visitation" teaching St.Elizabeth and the mystical phenomenon sorrounding their daily prayer and the food that they were eating can be found here in this link;https://www.ccel.org/ccel/emmerich/lifemary.xiii.html
In the case of Jeremiah God sanctified him in the womb to make him holy or received the sanctifying grace to restore the Divine friendship with God. But God take further action on Jeremiah to make him not only holy but "blameless or righteous" too by touching his lips to receive the Word of God to proclaim it. God healed Jeremiah of his "concupiscence" before sending him on a mission.This is like receiving Jesus Christ the Bread of Life or the WORD internally like the Holy Eucharist to cleanse his soul of concupiscence.
"Then the Lord reached out his hand and touched my mouth and said to me, “I have put my words in your mouth."(Jeremiah1:9)
For St.John the Baptist, he was fortunate to have a pious mother St.Elizabeth that was timely aided by the great intercession of the Theotokos to help her in consecrating St.John the Baptist.
We are seeing here a comparison, God in the Old Testament were consecrating the chosen souls and in the New Testament the Theotokos was now the one consecrating the chosen soul the last prophet.That's why among the promises of the Holy Rosary is "predestination". God in the OT was consecrating the "predestined souls" in Ephesians1:4-6 and after the Mystery of the Annunciation, Mary the Theotokos was now involve in consecrating the chosen souls for the gift of predestination.
"Devotion of my Rosary is a great sign of predestination."http://www.themostholyrosary.com/15promises.htm
In closing, St.John the Baptist and Jeremiah was both "sanctified in the womb" of their mothers. The major difference is St.John the Baptist nativity was celebrated by the Catholic Church Liturgical Calendar as a feast meaning St.John the Baptist was born like Jesus & Mary without original sin plus the guilt or stain of original sin was removed too. The Catholic Church does not defined nor teaches explicitly that St.John the Baptist was born without the stain of original sin but Jesus Christ proclaiming St.John the Baptist as the greatest prophet of all time and praising his Mother St.Elizabeth is the key to ponder.
Jesus Testifies about John
…"This is the one about whom it is written: ‘Behold, I will send My messenger ahead of You, who will prepare Your way before You.’ Truly I tell you, among those born of women there has risen no one greater than John the Baptist. Yet even the least in the kingdom of heaven is greater than he". (Matthew11:10-11)
We can infer thru the Wisdom of the Theotokos that St.Elizabeth and St.John the Baptist was praised by Jesus Christ because they overcome or was healed by "concupiscence" by the presence of "The Logos carried in the First Tabernacle overshadowed by the Holy Spirit". Truly the presence of the New Ark of the Covenant for three months in the house of Zechariah and St.Elizabeth do wonder of miraculous healing for their family. Zechariah was healed when St.John the Baptist was born and St.Elizabeth was filled by the Holy Spirit and aided by the great intercession of the Theotokos brought healing on their "concupiscence".
God put the Logos/Word in Jeremiah's mouth to heal him of his *"concupiscence".*While the Logos/Incarnate Word carried by the Theotokos on Her pure womb was brought to the pregnant St.Elizabeth to heal St.John the Baptist of his "concupiscence" while still inside the womb.
This is a great mystery to ponder and no wonder why the "Visitation of Mary to her cousin Elizabeth" was included in the Joyful Mystery.Now I know why it is very important to meditate the mystery of the Holy Rosary not just reciting it vocally. Again, Blessed Catherine Emmerich visions aided this answer to know why St.John the Baptist is the Greatest prophet in the biblical history.