It does seem to me that the republicans are so far out on the limb now, that they have to get some sort of concession or else they look like total fools. Of course, that is exactly how Obama and Reid want them to look, but the republicans have considerable leverage.
All this talk of no negotiating is hopefully just posturing, but with these idiots who knows.
The secret of successful negotiating is to find a way for the other party to come away with something without giving up stuff you need. Obama is loath to give up the one achievement of his administration. Plus he fears setting a precedent, where everything is open to budget hostage-taking. The republicans surely cannot just say "nevermind" and fold. So we have the most difficult negotiating environment, ie one side is determined to stand on principle and the other is determined to win something.
I think a fair compromise would be to delay Obamacare until after the next election in exchange for a republican promise to raise the debt ceiling annually as needed. This is not an ideal way to conduct business, but Obamacare was a sweeping change enacted on a party line vote. It's not like it was the result of some universal consensus. The many waivers, etc already given have undermined its legitimacy as well.