If they have a valid target, enough missiles will mission kill anything. I am not saying china now is capable of doing that, or that china in 2008 will be capable of doing it, maybe it is, maybe it isn't. I am just saying that in the specific case of 'fair' attack on a US carrier group (unfair would, for example, be killing it while docked in harbour, also immensely hard task i know) in the open waters you can go about it two ways: A) either develop such high tech to trump the tech used to defend the carrier - takes money and time (years or decades) and is dependant on various other prerequisites governed by politics, economy, etc) or
B) use a low tech approach with massive numbers of attackers. It is also an expensive way to go about it(albeit less expensive one, could be done with mere dozens of billions of dollars of investment, against at least hundreds of billions for option A), also taking time to prepare (doable within a decade, though) but one thing is for sure - human lives would need to be willingly sacrificed to get the job done. And i mean probably thousands of them. Of course, this approach too depends on political situation and the available number of suicide mission volunteers.