Mike Tannenbaum and Woody Johnson have pretty much destroyed what should have been a very promising era for the Jets. Rex isn't blameless and lord knows the majority of the "circus" headlines are down to him. But I think you'll find that those circus headlines weren't quite as bad when the Jets were actually winning and the winning was down to Rex.
Sanchez probably never had the personality to be an NFL QB, he showed he had the talent but his confidence has completely gone. He's pretty much an even more damaged David Carr at this point. His contract extension is one of the worst moves in the history of he NFL, probably second to acquiring Tim Tebow. For this Mike Tannenbaum should be shot. In the head. I don't blame us for picking him, the NFL is about getting franchise QB's, sometimes you have to swing and miss, but we kept swinging with this guy and pretty much swung our way into a coma. We have to move on from Sanchez now, 14m hit I think if we cut him and even more if we cut him the following season, so yeah we're fucked but we have to bite the bullet and take the hit now, that albatross has to fucking go.
As for Rex. I genuinely feel that had he had a good to elite NFL QB, he probably has two SB rings as our HC. He's all about defense, and although that limits him it's still worth it when the defense improves to the extent ours has under Rex. I'd give at least another year in a new regime, with a new QB, the only possible downgrade to Sanchez was acquired last offseason, so you can't really not improve. That young front on that defense is developing well, with Mo the fucking beast Wilkerson at the heart of it. I'd rather see Rex over that unit that just about anyone.
Edit: Also, as much as I hate Tebow as a player, I don't doubt he's telling the truth when he says Tannenbaum and Woody Johnson lied to him about his role. For all his flaws, Tebow is a good guy while Tannebaum and Johnson are very bad people.