A very big danger with a high debt (gross debt, using the terminology here), is the size of the interest payments. A very high debt, coupled with normal interest rates (or abnormally high interest rates (think early 1980s)) means very high debt repayment costs. The US has been lucky in the past 10 years or that interest rates have been well below what would be considered normal in an historical context. As a result, debt service costs have not (yet) ballooned.
When debt service overwhelms every other budget item, the government loses the flexibility it needs to, for example, cope with an economic downturn.
Canada faced a debt crisis in the mid-1990s. Their abnormally high debt (72% debt-to-GDP) sparked a credit downgrade by the ratings agencies (Moody's, S&P, ...). This sparked a round of severe belt-tightening - a combination of drastic spending cuts coupled with tax increases. Canada is much better fiscal shape as a result. It was comfortably able to deal with the 2008 recession (which was also less severe in Canada than the US).
People in the US forget that the US was running a surplus at the end of the 1990s. It turns out if you simultaneously cut taxes and start a couple of wars, a surplus will quickly turn into a deficit and the debt will increase.
At some point, the path that the US is taking (for example, cutting taxes while the economy is doing well), will get the country to a point similar to where Canada got to in the 1990s.