They won't ever be deterred from fighting China, because to them, China is the final boss. Defeating China is worth exploring any sacrifice in a way defeating even every single country besides China at once isn't.
In their more sober moments, US seemingly do recognize that they're weaker in quality and are all but guaranteed to lose in quantity too once China begins building up.
For example some US reports straight up rule out hitting anything on the mainland during a war, because they believe the IADS to be too strong for attacks to be worth it.
Then again, sometimes US will lose their grip on sanity, because they know the way they've set up their empire, they're all but guaranteed to collapse if they lose in Asia. They're not thinking rationally because it's their life on the line.
Again, this isn't rational skepticism. It's the life and death delusional skepticism of a gunman pinned down, seeing swat teams approaching. They will try and find any excuse to justify that they will walk out alive or at least able to parley.
Nuclear planning is no different than conventional planning, just by out-building and out-teching US, it will scare them even more. But even if scared, they will always fight because the alternative for them is worse.
However, they will never fight with nukes unless China does it first and/or makes intent clear they will wipe out US to the last. Because their leadership class will lose everything once nukes are used, which they won't if they make a conditional surrender.
Taiwan is just a trigger point for a greater Asia conflict. China will never stop at Taiwan if US empire invades, that would be like USSR stopping after reclaiming Moscowien and Ukraine from the Germans.
US is only able to claim Taiwan due to inheriting the claim from Imperial Japan. So the end of the war must be in Tokyo. The empire of the western world must be expelled from all Asian colonies they stole from China and those territories returned. That will not trigger a nuclear conflict, as US has lost no core territories.
On nuclear strategy, the current technology is not anywhere near good enough to proof against another nuclear superpower, but there are glimmers of hope as the newest defenses can apparently even take down HGVs. Imho China does not need capability to shoot down all ~3000 nukes to defeat US' nuclear capability, it only needs to have enough missile defense to force US to use everything on China to ensure MAD. Because once it reached that level, US will functionally be unable to ensure MAD against its other adversaries. As such, US will then never use it's nukes in (nearly) any scenario (because they know that if they nuclear holocaust China, Russia, Iran, even Brazil, India etc. will remain near 100% intact and can colonize the destroyed USA).
That strategy is admittedly hinging on US not building more delivery platforms.
