Krugman (here), Rogoff, DeLong, and others all have recent writings on this topic. My general view on these matters is the following:
1. There is nothing sacred about "90 percent" as a cut-off ratio and in any case such structural quantitative estimates are not stable over time. The accompanying expectations matter too.
2. The United States today (and in many other times) can manage a ratio higher than that; how much higher we do not know and what is the correct "stopping rule" we do not know. I suppose we will find out.
3. Major wars aside, if the United States approached or exceeded the 90 percent figure, it would be a sign of a dysfunctional politics and an irresponsible citizenry. Do we have to borrow that much money? Can't we just pay for the stuff? Apparently not.
4. Even if the debt is not itself a problem, being skeptical about the debt is one way to enforce accountability on the expenditure side, namely by requiring transparency on expenditures and who is really footing the bill for what.
5. If the United States reaches or exceeds that ninety percent ratio, which is likely, it will be because of health care costs, spending too much on health care, and having dysfunctional health care institutions.
6. Under the scenario of #5, measured gdp might do OK. Health care costs are part of gdp too. But we will be misallocating resources on a massive scale and the high debt helped make it possible.
7. At some sufficiently high debt-gdp ratio, it becomes a foreign policy issue and a big one. Postwar UK had a high debt to gdp ratio, and to this day it is a fine place, but that debt meant the end of England as a world power, for better or worse. The U.S. for instance used financial issues to push England around and they basically had to give up on their overseas commitments. A very high debt ratio here would mean the end of the U.S. as a global world power, again even if gdp does OK. A global power needs the option of spending a lot more, quickly, without asking for anyone's permission. Your mileage on a U.S. retreat from the global policeman role will vary, but it's the elephant in the room which hardly anyone is talking about.
8. I don't agree with Jim Buchanan on either a balanced budget amendment (I am against it, preferring deficits in recessions), or on the intergenerational incidence of domestic debt. Nonetheless his writings are an undervalued resource in this debate. Very often he focuses on what debt does to a country, drawing upon the Founding Fathers, the classical economists, and the Italian public finance theorists, among others.
Addendum: Ezra Klein comments.