First, interest will go up. US Bonds are now considered riskier than they were before. This means investors in US Bonds will expect to collect more interest due to the greater risk they are taking. Instead of paying China and Japan 3% (for example) on $1 trilion (each), the US will now have to pay 3.5% (and climbing). Of course, the higher the interest rate, the harder it is to pay back (the quicker a new ceiling is reached), the likelier this happens again.
There could be some pretty massive dumping of US bonds. A number of foreign investors can only carry AAA risk. (It's kinda unclear where they'll run to though, since I think all the other AAA countries combined don't issue as much debt as the US). So, the economy might take a pretty big hit by losing all those investors.
Now, generally you need 2 of the big 3 rating agencies to trigger any of this. So it remains to be seen whether Moody or Fitch will follow. I think they both will.
Also worth mentioning is that Canada recently came back from a downgrade (by S&P) mostly by tightening their spending belt. Took 10 years (1992-2002). Australia did it too, though it took 7 years longer.