In his speech to King Agrippa, Paul describes how, immediately after his call by the Jesus, he began to preach, first to Jews and then to Gentiles, “that they should repent and turn to God, and do works meet for repentance (ἄξια τῆς μετανοίας ἔργα πράσσοντας)” (Acts 20:26). There’s a clear echo here of John the Baptist’s snarl to the hypocrites who came to hear his preaching: “ποιήσατε οὖν καρποὺς ἀξίους τῆς μετανοίας” (Lk 3:8, cf. Mt 3:8). In light of that, it’s doubly striking to me that the Paul of Acts refers to the Baptizer in his (very early) sermon at Pisidian Antioch, as one who came before the Christ with a “baptism of repentance” (Acts 13:24-25).
Here’s an interesting thought: Acts represents Paul as having been educated in Jerusalem (Acts 26:4, i.a.), and as having been there in the early days of the Christian movement (Acts 26:10, i.a.). There’s no question that John the Baptist was at least as famous as Jesus during their careers, and for some time thereafter (Paul discovers a small group outside Ephesus that have been baptized by some itinerant preacher, probably Apollos, with the baptism of John, cf. Acts 18:24-25, 19:1-4). Perhaps the fact that Acts seems to posit an unusual (by the standard of the epistles, that is) connection between Paul’s early mission and the Baptizer indicates that Paul himself had some kind of connection to John, that his early Christian preaching was worked out in terms of a similar message that he knew better.
This is speculative of course, but that’s what makes it fun!