Either the US government receives, from Congress, dispensation to increase US federal government debt above and beyond the $14,294,000,000,000 limit it currently has, or, given the current rate of increased debt acquired by the US government, in 45 working days, the US government will not be able to add to its debt, as the current debt (as of 18 May 2010: $12,984,667,000,000) will, at the current rate (some $27,000,000,000 per day additional debt), exceed this limit.
Either Congress has to raise the debt ceiling or the US will not be able to go further into debt.
That's today in nine weeks: 22 July 2010. Will Congress even be in session on that day?
Given the present Congress, I dare say that the credit limit will be extended. However, it doesn't change the fundamental fact that US debt is climbing at an unsustainable rate and that a day of reckoning will be coming.
Source: Daily Treasury Statement of the US Treasury (see here), own calculations. See Table IIIC.