So, yeah, if we're pummelling the snot out of some small country (Grenada, Venezuela, ???) and they get off a lucky shot with a missile or torpedo that manages to sink one carrier, then a nuclear response would be unwarranted and unlikely, and we'd just see continued conventional operations by the rest of the fleet.

But that scenario is so unlikely. But we're realistically talking about an all-out attack on a carrier group with ballistic missiles or nuclear subs, possibly with nuclear warheads. This would only be mounted by a Russia or China. Or possibly Iran trying a swarm attack with thousands of small suicide-boats. This would be in the context of a much larger war and operations.

Attacking a carrier group is an undertaking of huge magnitude - a huge escalation in itself, and anyone should expect a serious response from a successful attack. And, keeping open the question of whether that retaliation might be nuclear is also an important deterrent.

The context would certainly determine whether or not it actually goes nuclear. E.g., what other resources can be brought to bear, under what threat is the rest of the fleet? E.g., if it was the Chinese ballistic anti-carrier missiles, and we knew exactly where they were and could target them conventionally, we probably would, but if they threatened the rest of the fleet, and the only way to neutralize them was nukes, ... watch out.

So, overall, I'm not saying it would necessarily be nuclear, but it certainly wouldn't be surprising if it were. And, if it were, I'd expect that it would be seen as not un-reasonable, because if the US follows its own history, we're very reluctant to launch them.