So right now the GOP is getting slaughtered by their base for the fiscal cliff deal. That means they will have to come in on this guns blazing, zero compromise, and force a default just in order to protect their right flanks in 2014.
That's a tough order for them, and may further alienate them from the center (which fortunately doesn't matter as much for midterm elections).
I think that means than anything other than complete capitulation from Senate Democrats means we risk default. I put that at about 90% likely that we will not have a deal by the deadline.
If that's a case, Obama will absolutely have to take some unilateral action. One option
Under the current law, the executive branch of the government (which includes the Treasury and the President) is obligated to carry out all appropriations authorized by the Congress. It has been argued that, in the presence of conflicting statutes (a federal budget statute, which instructs the Treasury to spend a certain amount of money, and a debt ceiling statute, which limits the amount of money that the Treasury is allowed to borrow in process), the statute that was passed more recently "wins"; therefore, in this situation, the President may simply instruct the Treasury to continue issuing bonds beyond the ceiling. Furthermore, such an instruction may be difficult to challenge in court, because it would take a joint resolution of both chambers of Congress to get standing to challenge it. In addition, it has been observed by many, such as legal scholar Garrett Epps, fiscal expert Bruce Bartlett and Treasury Secretary Timothy Geithner, that the debt ceiling itself may be unconstitutional and therefore void as long as it interferes with the duty of the government to pay interest on outstanding bonds and to make payments owed to pensioners (that is, Social Security recipients).