My guess is the Jets head into the draft without signing a FA QB. If they draft a QB early, they'll let the rookie and Sanchez battle it out. Worst case, Sanchez wins the job, while the rookie has a year to groom on the bench for 2014.
If they dont draft a QB, I'd see an early summer scrap heap QB signed on a 1 year deal to give Sanchez competition. Winner is the QB for 2013, and the Jets reassess their QB in 2014 when they finally have the cap room.