There's is no scenario where Russia loses this war and Putin doesn't lose power and therefore, probably, his life. Not after Friday's display. So, that probably informs a lot of his thinking. And he doesn't really have any other cards left to play as I see it.

The best (but still bad) US/NATO response is probably a conventional intervention, impose a no-fly zone and basically try and physically prevent any further nuclear strikes taking place by shooting down the planes and missiles delivering the strike (Russia probably would not use their ICBMs because the US would detect the launches, assume they were directed at them/allies and then we know what happens next), but this still carries just as much risk of escalation as it did when Ukraine was asking for it back at the start of the war.

Normally, I'd say these are just empty threats. Empty threats are sort of Russia's whole thing at this point, but with Putin doubling down on doubling down and the military situation rapidly for Russia I actually think there's a non-trivial chance they might do it. Unless, of course, all the warheads have been sold to pay for yachts.