There is no chance of a debt default. None, zero, nada. The government has the funds to pay its interest obligations on the principal they owe, and, if necessary, and it will be -by design- they will take what they need to pay debt obligations from government programs as per the dictates of the 14th Amendment. That is what will transpire assuming they don’t reach an agreement. However, an agreement will achieve the exact same thing as no agreement, except less messily, as it will involve decimating those very same government operations that will be plundered if there isn't an agreement. That’s what I call checkmate, mate. Heads I win, tails you lose.
My bet is that they will come to an agreement because Obama is just another neo-liberal shyster sellout. The third rails of U.S. politics were/are thought to be certain entitlements and military spending. In retrospect it will be clear that when the chips were down it was only the latter that was untouchable not the former.