Two points...

1. If you owe the bank $100, then that is your problem. If you owe the bank $100 million, then that is the bank's problem. We owe trillions of dollars to the world. If something happens that makes us unable to make timely payments on that debt, then it will become the world's problem.

2. Too big to fail.
If the US ever suffered a significant depression or other economic calamity then the world would need to think of something quick, because our economy is "too big to fail." If we go down, then Japan and China are going to be holding some worthless paper, oil producers are going to see demand plummet, every country with a current account surplus is going to be living off of its reserves, Africa and the UN get no more money, South America gets the double whammy of no more aid and less demand for their illicit drugs, and Europe can try to piece it all together while supporting their welfare states.

If America is in decline, then the world is in decline.