Gaming this out,
The Teabagger Caucus simply will not sign any deal that increases the debt limit. They hate Obama and know they can cause his failure by doing enough damage to the country.
The rest of the Republicans would be willing to extract a pound of flesh and move on, but they fear the Teabaggers. In particular, Boehner knows his political career is over if he merely wins this one, rather than triumphs. The Teabaggers would force an immediate leadership challenge.
The Dems in the House under Pelosi seem to be vaguely aware of the fact that signing off on a deal that destroys the economy as all of the deals proposed so far would -- would be bad for their reelection prospects. So they're leery of even the "pound of flesh" result.
On the Senate side, Reid would need something like consensus levels of agreement (80 Senators plus) to thread any deal through the Committees and onto the floor in less than a month.
I'm concluding here that no deal is possible, and that doesn't even get into Obama's vague desire to make his run at SS and Medicare during the crisis.
Either Obama invokes the 14th, or we default. That's it.