Going by historical policy, we'd have the carrier group in the waters beforehand if there was any sign of impending hostility. An attack on the carrier would probably result in retaliation against military targets.

That wouldn't need to be nuclear. We still have rather a few submarines for use against capital ships, invasion ships, etc. If they can do it, we can:

http://www.dailymail.co.uk/news/article-492804/The-uninvited...

Sadly, the very point of a stealthy submarine makes it useless for what a carrier group does very well - signify military presence and imply the willingness to use it.

Of course, carrier groups often include submarines. Perhaps in the future, carrier groups will have more submarines to get around the ballistic missile threat. Take out the carrier, and you've just blasted off the visible part of the iceberg, no more.