Nothing. A Nuclear Bluff is just that, a Bluff. Putin can't win in a nuclear war and if he uses nukes anywhere, he is done for. No one is going to have anything to do with him or Russia on any level after that.
Lets say Putin nukes a carrier group at sea. This wont trigger an immediate counter attack like launching ICBMs would. Biden/whoever would have to order launching the nukes. Follow this for any usage of tactical nuclear weapons.
Will he decide to end life in America and most of the world over a carrier group? There's a non zero percent chance he would flinch at that.
Your argument is that nobody would have anything to do with Putin, but we already pretty close to that point. Backing Putin in a corner makes him MORE dangerous, not less.
Putin could do all kind of things to completely undermine as well. What happens if he decides that the world uniting against Russian means Russia no longer need to adhere to the Non Proliferation Treat and offers "free" nukes to whoever aligns with his new order? It's already understood geo politically that "no nukes" means the West and China get to bully you whenever they want. So why not take the offer? There's all kinds of ways this could get worse without all life ending.
I really doubt it. At the bare minimum a nuclear strike on military targets would provoke nuclear strikes on military targets in response. Excepting the middle of oceans, that's going to involve major civilian casualties. And then we're back to doomsday.
Not to get all Dr Strangelove on you, but once the nukes start flying there's really only one option - immediately take out as many of your enemy's weapons as possible. Sink all submarines, nuke all silos, hope for "no more than ten to twenty million killed, tops, uh, depending on the breaks."
Especially if a purely military target was hit like a carrier group and it was all soldiers that died?
Its not so obvious to me that every leader could do that.
Now look at the opposite. You are a leader who is about to be killed/ousted/lose everything if current course continues. No matter what you are probably dead in 10 years anyways due to old age. Why not? Especially if you think Putin is how he is portrayed by Western media?
Not sure what culture you grew up in, but I grew up in the "progressive" side of the US and I'm quite certain that even the folks out here would demand immediate retaliation. The folks that grew up in red states are even more bloodthirsty. At minimum we'll be using nukes against Russian military targets, and I just don't see that de-escalating.
We don't know what he would do. A desperate dictator might just use nukes.
There's also the greatly increased risk of accidentally starting a nuclear war -- something we've come close to multiple times, even in peace time. In war time that's just short of WW3, the risk is increased exponentially.
No sane person wants to gamble with the literal fate of the world. Yet both sides are doing this by getting this close to WW3... that doesn't lend confidence to the possibility of staying out of a nuclear war if NATO "calls Putin's nuclear bluff".