If we go to war with the Chinese, I FIRMLY believe that they would NUKE our carrier forces, then pick off the other ships.
The carriers are a projection of incredible power. I'm sure the loss of a carrier group or two would be worth a couple of cities to the Chi-coms.
Remember what the Chinese general said just before they entered the Korean War, when asked about the possibility that the US government would retaliate with nukes. 'So we loose a few million people. We can afford it.'