Sure, but failure to secure at least a short-term solution to the debt limit issue will only weaken demand for US debt, raise interest rates, and thus worsen the situation.
It doesn't mean you default, but default is one possibility (which Obama may unwisely calculate to be less politically damaging than diverting SS checks or military paychecks to pay creditors), the market is aware of that, and as you pointed out at the end of the last thread, much of US debt turns out to be short-term bonds that will be quickly affected by the increase in interest rates caused by lack of market confidence.
Raising the debt limit is not the solution, but is part of the best solution - a balanced budget attained via significant cuts in military spending, increased revenue from the top 0.5% (ie. not the six-figure professional crowd but the seven-to-eight-figure-earning financial parasites), perhaps adjustments to SS and Medicare/Medicaid, and resolution of this manufactured debt limit crisis (there is a problem but, as you point out, it's not a new problem) to demonstrate to the world that we are still a country run by mature adults.