The carrier wins the maneuverability race.
In order to hit a carrier it would then have to be a huge conventional blast: on the order of 30,000 lbs of TNT within a 1/8 mile radius. Not a practical load for an RV.
The carrier wins the blast race.
It would therefore, at a minimum, that the RV be nuclear in the 5 - 10 kT range. Doable, but then you bring the entire US nuclear umbrella down on your head.
We loose a carrier, you loose your country and a few hundred million to nuclear strikes.
We win and send the Marines in to polish the glass of the new worlds largest optical telescopes.
If you want to defeat a carrier strike group, ignore the carrier. Go after it's defensive armada.
If the destroyers, cruisers and subs are gone, a naked carrier is no threat.
You have to be able to track and respond quickly enough to maneuver, and the carrier certainly won’t be doing the tracking so that means the combined carrier group assets, the ABs and their Aegis radars would have to do it and then get the data to the carrier quick enough and for them to respond. I don’t think they could do it personally.
And if you think Obama is going to respond to anything with a nuclear response, then I don’t know what to tell you.