While the markets don't give a fig about S&P's analysis of the creditworthiness of US debt, it does appear to fear that governments will be pushed to follow S&P's bad economic advice:
The downgrade of the United States’s debt to AA+ from AAA has global implications, said Alessandro Giansanti, a credit market strategist at ING in Amsterdam. “We can see that this may force the U.S. to move more aggressively to cut spending,” he said, something that could drive the already weak economy into recession and weigh on the economies of all of its trading partners. “That’s the main driver” of the stock market declines, he said.
Krugman makes a similar point:
[M]aybe there is an S&P story — but not the one you think. Arguably, that downgrade will bully policy makers into even more deflationary, contractionary policies than they would have undertaken otherwise, which has the perverse effect of making US debt more attractive, since the alternatives are worse.