If another recession does take hold, it will be a nasty fight.
Yes, possibly literally. Major wars are often the ultimate solution to this kind of problem. When the dust settles a new order exists.
I detest war. I detest human suffering. But it appears sometimes war has amazing cleansing power. Hopefully this isn't always the case.
Alas, there seems to be always at least one party that is opposed to any kind of visionary project.
The US federal government, on the other hand, is the issuer of USD. If it wants to make a payment in USD, then nothing can stop it.
This means that the debt-to-GDP ratio is an entirely meaningless measure as far as the government's ability to fight a recession is concerned. (It may have play a role in other consideration, such as questions about equity and distribution of wealth, but that's a digression.)
I remember when TARP was up for debate. It was obviously needed, and it was the right idea (as proven out by its success). It still failed in the first vote in the House, because it was politically unpopular with enough people.
the dept to GDP ratio (as well as printing money) has a huge effect on a countries ability to issue bonds, just ask the PIIGS. interests rates on bonds would rise very quickly making the annual deficit larger and since all interest rates in the country are based off the US treasury interest rate (the risk free rate), they would rise too, even if the US' interest rate was at 0. that'd make any recession get out of control as credit froze up.
it'd be the fed's worst nightmare. they would loose control of interest rates during a recession while the central government would loose its ability to borrow money.
Other than that, I can only recommend that you try to consider all the relevant dynamic effects in the macroeconomy. For example, if money would indeed become worthless, this would not happen overnight due to the immense inertia of an economy as large as the US economy. It would be a drawn out process.
Throughout that process, as a consequence of money losing value, the nominal GDP would increase, and therefore the debt-to-GDP ratio would decrease, which means that the system has a very strong self-stabilizing tendency.