Today I've read (don't ask why) some interesting assertions that not passing an increase in the debt ceiling would actually be okay, and wouldn't really spell doom for the US's economy. The crux of the argument from the "don't-believe-the-lies-about-the-debt-ceiling" crowd seems to be that payments to all creditors could still be made (thus ensuring that the US avoids technical default) so long as government spending on goods and services is immediately cut by a sufficient amount to balance the budget. Since we can't get the politicians to agree, we let the debt ceiling force spending to be equal to revenues and presto, instant spending cuts and balanced budget!
Actually, yes, there's some sort of point there; I suppose it might be possible to continue to make interest payments on the debt even if the debt ceiling isn't raised, because revenue inflows are sufficient to cover those interest payments -- so long as you can instantly cut federal spending by $1.3 tr. annually.
Just for fun, let's imagine that we can simply stop sending out checks for $1.3 tr. worth of government purchases without actually getting into the situation where the US government isn't paying someone what they're legally owed. Let's imagine what that would do to the US economy.
A cut in spending translates into an initial fall in economic activity by an equal amount; cut $1.3 tr in government spending, cut economic output by $1.3 tr. (There's no crowding in effect when interest rates are at the zero lower bound, after all.) So overnight the US economy suddenly shrinks by about 10%. For reference, during the recent recession the US economy only shrank by 3%. Oh, and then over the coming months a couple of different multiplier effects would kick in, causing output to drop further.
If economic activity has fallen by 10% or more, it's reasonable to think that employment will fall by roughly the same amount. So we can expect about 10 million people to lose their jobs in very short order, bringing the unemployment rate to close to 20% of the US population. And then it would probably rise from there as the multiplier effects do their thing. For reference, during the recession the unemployment rate peaked at a lowly 10%.
Ah, interesting; we could all have the experience of living through the Great Depression, only this time it would have been caused intentionally...
UPDATE: text edited slightly for clarity.