Not very likely, unless Obama either;
A) Refuses to cut a deal and the debt limit expires, which sends the US into default.
B) Issues and Executive Order that unilaterally raises the debt limit without Congressional approval.
Personally, I think the first scenario is exactly what is about to happen, as far as any deal being reached.
What Congress does after that I couldn't guess.
Hell, even they don't have a clue what they're going to do.