I have no doubts we can get the thing whenever we wanted her...but it may prove costly. Maybe better to let the naval fly boys, or the air force guys off Guam take her down...but they would have a gauntlet to run too, with Chinese air and the new area air defense DDGs they Chinese are pumping out.
They will hope to make it appear too costly to a new administration is my bet.
Jeff,
Using an aircraft carrier in confined littoral waters is useless. You might as well use land based aircraft. An aircraft carrier is an open ocean power projection weapon which has utility in the littoral battlespace as an attacking platform. There are many ways to kill a carrier you can use Tomahawk, Harpoon, Harpoon SLAM, SRAM and evem ALCM's among other things. All of these can be lauched from a number of different platforms. Equippped with the right warhead you can even take out a task force.
I bet we could put more missiles in the air than their AD DDG's can handle (attack from many platforms [air,surface,undersea] with different weapons,no defense shield is impervious)and many of the missiles we would shoot would be targeting the escorts first. Once you take them out it gets interesting.
Fighting in the PRC's litoral could get sort of strange. Most Americans are not very familiar with the area. They picture something like one of our coasts - with low densities of civie ships and wide expanses of water. In reality, with the many, many shoals, small islands and generally flat water, combined with the zillions of potential targets, it would not be straightforward. For example, is the barge with one container on it what it appears to be? Etc ...