We're specifically not talking about attacking the carrier with nuclear warheads. We're talking about the US initiating nuclear war in response to a conventional attack on a carrier.

And don't underestimate small countries. In an exercise (a long time ago), a Dutch diesel-electric sub "killed" half a dozen US ships, including a carrier. Nuclear subs aren't much of a threat to a carrier (because they're noisy), but diesel-electrics are one of the few weapons that are known to be able to get close enough, because they can be extremely quiet.