Caveat 1: I think they stand pat and take a QB at 3.
BUT, and understanding that it's not without risk (and without going into all the possible permutations why I think this is possible), it's still likely that NE can get JJ at 11, or worse case Penix/Nix (notwithstanding the team hasn't shown much if any interest in either.)
Pro: They end draft day with a QB they like, a (likely) starting LT and very good WR (or trade 34 for Higgins) + an extra 1st round pick next year. (It will be much harder to get both a starting OT and a WR with picks 34 and 68.)
Con: They get a lesser QB prospect.
Caveat 2: Trade would be something like 11, 23, 4th, and next year 1. That's an overpay but needs to be in order to move down