The calculation on the part of the Chinese is that yes, America would sit idly by while it watched on CNN 2 or 3 of its nuclear powered aircraft carriers spectacularly sink under a hail of (admittedly inferior) anti-ship missile fire. The same way we watched the evacuation of Vietnam.
North Vietnam traded 600 thousand casualties for political positioning in a long-term play. China is willing to trade almost 20 times that number of casualties.
I think the timetable is some time in the next 15 years or so.
Recall the USS Stark, which went down from only 1 missile fired from 1 aircraft and it was supposedly in readiness state (hey, it was an Iraqi plane that sunk it, I almost forgot). It isn't that much of a challenge to overwhelm the defenses of a ship at sea. After that, it is a direct tradeoff in blood.