That salvation was to be found in Jesus Christ was a proposition to which Paul and his Judaizing opponents would equally have subscribed. They might even have agreed that salvation was to be found in him alone. But on what conditions was the salvation found in Christ alone to be secured? This was the crucial question. No doubt Jesus did sit very loose to the traditions of the elders, but when it was a question of the admission of the Gentiles to the fellowship of his disciples, could Paul or any one else seduce a single utterance of his which suggested that circumcision could be dispensed with? (Indeed, when we consider the important part played by the circumcision question in the development of the early church, we may be impressed by the absence from our gospel tradition of any attempt to find a dominical ruling to which one side or the other could have appealed.) Paul might have appealed to the spirit of Jesus’ teaching, or (as he did) to the logical implication of the gospel, but people like his opponents would be satisfied with nothing less than verbatim chapter-and-verse authority, and this was not forthcoming.
(F.F. Bruce, The Epistle to the Galatians [Grand Rapids: Eerdmans, 1982], p. 38)