The US is taking seriously a threat posed by Chinese efforts to turn an ICBM into a aircraft carrier killer. Assuming the targeting could be worked out, which is a large assumption, an ICBM with a conventional warhead could be effective against large ships. The high speed and angle would make it difficult to stop. It is the same difficulty we are facing in setting up an anti-ballistic missile shield. The missiles that we are aiming to stop are ones tipped with WMDs, primarily nuclear weapons. Once we have an effective defense against one we will have an effective defense against the other because they are the same thing just with different war heads.
Of course, the Chinese would not have to worry as much about the targeting of these ship killers if they were nuclear tipped. That would just speed up the process after all. The first problem is that the US would not be able to tell if the missile was nuclear tipped until it reached the ship. The US could have already responded to the perceived threat. Also, what do they think we would do if they were to successfully sink a carrier and kill 5,000 Americans? The back and four from that could easily turn nuclear.
More at http://blog.wired.com/defense/2009/03/china-turning-m.html.