If I'm not mistaken, our doctrine is that any nation which takes out one of our carriers received a nuclear counter-attack. We don't have a lot of events which trigger a US nuclear response, but I believe sinking a carrier is one of them.
In other words, any foreign nation which seriously attacks a US carrier is going "all-in" and WWIII has begun.
While I believe the current occupant of the White House would give a (limited) nuclear reply if one of our carrier task forces was nuked, if a country somehow took out a carrier with conventional weapons I suspect he would only respond in kind.
No way is Obambi in for that. He will defer to Eric Holder.