I really think they don't have much of a choice at this stage, assuming the cap hit wouldn't be too terrible (not sure when his contract is up). He has regressed every year and the Jets just need to start over at QB.
Actually, if he was on his original rookie contract, it would have been up after this season.
However, they signed an extension through 2016. From what I've read, it would be prohibitively expensive to cut him this coming off-season (cap hit north of $10 million, when they are already $7 million over the cap for 2013). They could trade him, but I'm thinking it might be hard to find a taker for Sanchez even with a reasonable contract ($8-9 million per year plus bonuses).
However, they can cut him after the 2013 season since the 2014-2016 are essentially option years.