While China can nuke/sink a whole carrier group, it can just take out the carrier without a nuke. It would likely be a response to US sponsored aggression rather than pre-emptively today. The US empire does require its existence by having its citizens believe there will never be a threat to Americans or the empire, and that it deserves to win. That is why history needed to start on 9/11, with "they just hate us for our freedom".
It would be unclear if US fleet or Tel Aviv were destroyed in a chosen war of aggression on Iran, requires a NATO meeting or tolerance for US evil/empire. If US were to send a carrier fleet to prevent Korea unification, that sinking it becomes a NATO matter. EU is on extreme thin ice for their demonism over Ukraine, already.
Pretending that the US can protect their populations is what justifies sycophantic colonial rulers sucking up to US on every issue. Hegseth telling their populations that US is impotent, makes the corrupt enslavement of the colonies people to the US more difficult.
No one has made a threat. Exercising capability is a hot war. The only people who made any comments are the Pentagon. Admitting that the US is impotent losers is a bold move, Cotton. This is the cold war now.