After talking to way too many economists, how it's going to shake down is pretty inevitable. The necessary tax revenue raises or spending cuts to balance the budget or simply bring it down to sustainable debt levels is basically not politically feasible. Imagine taxes more than doubling (tax rates would have to go higher, as you have diminishing returns as you raise them), or more than half of all government spending being slashed.
Simply put, no economist really believes this problem will be fixed. Or likely will be.
So what's probably going to happen is, things will continue exactly as is. Minus some political theater, a token spending cut or tax raise. So, the debt will grow until either folks stop buying and/or the US can't make the interest payments. Along the way, the US credit rating will drop. This doesn't mean much, actually, except that interest rates on the debt will have to rise (else people will not buy as many).
The credit rating dropping would be a good thing for the US government in the short term, as more folks would be willing to invest their money at a higher rate of return. Credit card lenders are not extremely happy with folks with perfect credit, and thus low interest rates. Bad news is, that's higher interest payments. Servicing the debt becomes more expensive.
Along the way, there are certain stopgaps that the US Federal Reserve and US Treasury will do. Inflate the money supply, dork around with inflation, try to dork around with interest rates, etc etc. These are tactical decisions, not strategic. They'll change the timetable but not the end state.
If nothing changes, the US will simply continue to borrow until no one will lend to them or they cannot make payments. Not making payments is probably the more likely, but it'd depend on the world economy at the time. After trying all of the time buying tricks, that will be the day where reality hits home.
The US will default, inflate away the debt, or take the financial responsibility path. Defaulting is relatively straight forward, they simply do not pay the interest and/or refuse to redeem any outstanding treasury securities. But this would also piss off a very large number of foreign countries, corporations, the entire financial community of the world, and pretty much anyone with any investments whatsoever to include pensions. Many pensions require a portion or all of the pension investments to be in US government securities. Inflating away the debt with extremely high inflation is possible, but political suicide for any incumbent due to civil disturbances and loss of quality of life.
Financial responsibility would be a mix of draconian spending cuts and revenue increases, driven by lack of other options. This may actually be the most possible out of the three end states, but I personally believe it will be a mix of all three slapped together in desperation.