An obvious question, should Congress not manage to fend off default within the next two weeks, is: What does the President do then? If the President cannot pay off America’s creditors and keep all government programs running, what legal authority does he have to deal with the crisis?
Answers at What May a President Do if He Cannot Pay Our Bills Without Borrowing and Borrowing More Money is Unlawful?.
The bottom line is that the President has a pretty free hand to “defer” any spending he wants — an ironic given decades of Congressional attempts to stamp out claimed executive “impoundment” authority and force Presidents to spend as directed by Congress.
The only thing I’d add to Peter’s story, which is worth a look, is an historical note: the 19th Century budget process also relied on something called the Anti-Deficiency Act (which still exists in somewhat amended form. The basic idea behind the early versions, was that if anyone in Treasury paid any expenditure not authorized by law (which then meant an appropriation), the official risked being personally liable for any overpayment.