Most economists agree that when the national debt is double the Gross Domestic Product, that the point of no return will have been reached. At that point; no amount of growth, spending cuts, tax increases will be able to alleviate it, and that the US will have to start defaulting on some of it's debt.
What that actually MEANS is unclear. The collapse of the American economy would doom the rest of the world for a LONG time, so it's doubtful that they'll strong arm the US. Probably a mixture of renegotiated terms and debt forgiveness would happen.
The US is unique, in that it is probably the only country that could declare bankruptcy and still recover within a generation. We're impervious to a military takeover, and we've got enough domestic resources to go all in on isolationism.