I'm not sure, honestly. I certainly think it's a risk that the next big war starts, it goes poorly for America, and then we resort to nuclear weapons to squeeze out "victory" (i.e. everybody dies) if we're all going to die anyway.

But I think there's another possibility that most people aren't considering: disintegration. It's very common for countries to cease to exist as countries when they start losing a war, particularly a war that happens because they're moribund and falling apart internally anyway. Witness the Austro-Hungarian, Ottoman, and Russian Empires in WW1; the end of the Roman empire; England during the War of the Roses in the aftermath of the Hundred Years War; Yugoslavia and the Soviet Union in the wake of the Cold War; etc. This also doesn't have to wait until the end of the conflict: most of the big disintegrations in WW1 happened in 1917, before the armistice, and sometimes even to "victorious" parties.

Modern nuclear weapons are very tightly controlled with PALs, so that you physically can't arm them without correct codes produced by the Pentagon/NSA bureaucracy. If that bureaucracy falls apart, it's likely they will just rot in their silos, while humanity dukes it out with relatively primitive technology because nobody wants to work together anymore.