I agree with MJ. Tannenbaum should absolutely be gone. I think Rex is a solid coach, really good defensive mind, and I could see him being a good NFL coach. I don't care for all the bravado personally, but he certainly does have a lot of pluses otherwise.
He seems like he's lost a lot of confidence and the team, however. I'd give him another year or two and see how it goes. If he doesn't end up sticking with the Jets I think he'll find success with another franchise at some point.