They'll downgrade US debt from AAA to D if the US misses a payment:
"If the U.S. government misses a payment, it goes to D. ... That would happen right after August 4, when the bills mature, because they don't have a grace period." The company would downgrade Treasury bills unaffected by the blown deadline, but not as much.
If you thought it was bad when AAA mortgage-backed securities turned out not to be AAA, just wait to see what happens when the full faith and credit of the US government is no longer credible. At that point, banking regulations under current definitions become essentially meaningless, since capital weights and risk-pricing models use "risk-less" Treasuries as their baseline. Using Treasuries as highest-quality collateral ends, and balance sheet accounting becomes a bloodbath. Under current capital requirements, which banks wouldn't be immediately insolvent if Treasuries went to D? I can't imagine a scenario in which this would not lead to a bigger financial crisis than 2008.
The international dimension is also important. China will be very, very unhappy, as you would be if your "safe" $1tn+ investment turned out to be not-so-safe; battered banking sectors in Europe and elsewhere would take another (bigger) hit; if the US banking system goes, everything else goes with it. This could be Creditanstalt times a thousand. Or a million. I don't even want to think about it.
Republicans seem to be worried that continued deficits will weaken the credibility of the US, eventually leading to higher bond rates. However, a default would guarantee that outcome immediately and catastrophically. It's like shooting yourself in the face today to prevent your future self from being mugged.
I'm not as pessimistic as many others concerning the US political system, so I still believe that a deal will get done*. And I understand that dancing closer to the edge of the cliff can be a good negotiation strategy**. But it's also perilous.
*Surely the GOP realizes that if they blow up the global economy not a single one of them will win re-election for a generation.
**All those people who said that IR work on nuclear deterrence was irrelevant post-Cold War might want to reconsider; this is the nuclear option.
[UPDATE: Here's Geithner's letter to the GOP. Nice invocation of Reagan. Nice job of telling them that they either don't know what they're are talking about, or are gambling recklessly with a precious resource.]