Good question. I would think that the US national debt can't keep increasing as a percentage of GDP while the US dollar maintains its value relative to everything. If the trend continues, then we either default on the debt or print lots more money, inflating away the value of the debt. Either one hurts the value of the dollar. If other governments behave similarly, then their currencies should lose value also. In this case currencies may maintain value relative to each other, but should not relative to hard assets which aren't in arbitrarily large supply.
So with the growth of the debt over the past 30 years, why hasn't this inflation occurred yet? So far investors have retained faith in the solvency of the US government...in its ability to tax and raise the funds it needs to service the debt. But the government hasn't been increasing taxation to service the growing debt. It has been increasingly borrowing to service the debt. As long as that faith in the US govt's ability and willingness to repay debt remains, the system works. But at what debt level (multiple of GDP) does that faith start to crumble, when the debt is so high and the govt's backbone so weak that British and Japanese and Chinese investors start unloading US debt? That's the point when the sh!t hits the fan and the value of the dollar crumbles.
Who knows when that happens? Maybe the US dollar keeps looking like the most stable instrument in which to store capital for a long time to come. After all, investors are looking for the most stable place, and that means relative to other available currencies. Still, if every country follows suit and builds up debt that they are unable to repay, and thus the US continues to look the most stable, whoever holds all that debt is eventually going to take a haircut, either by inflation or by default.
So I guess the OP's question is really about what happens to the US economy when the faith of US Treasury investors falters. Are we almost there? Is it still far, far off? Or will it never falter, and the US will be able to continue overspending forever with no consequences (like Rome)?