REALLY! And in response to our response, they'd level a few more American cities while they're at it. You think they're weapons are sitting in a personal storage facility we can take out with one hit? By the time we're responding to the first attack, their submarines will be ready to put an end to our republic, too.
MAD is great on paper. If responding meant a full blown exchange, I'm afraid we'd choose to absorb a hit in order to prevent the rest of the country from becoming an uninhabitable wasteland. The object is this: don't get to the point where China believes it needs to launch a first-strike ICBM at us out of defense. That may be unavoidable under some circumstances in the world, but Taiwan is hardly worth losing Seattle, Los Angeles, San Francisco, Denver, and Dallas over. If you don't think they haven't wargamed this out, you're crazy.
...We have agreements with Taiwan to defend them if attacked by China period.
Agreements are so much toilet paper in the threat of a nuclear exchange. If the Pentagon determines the risks are too high either conventionally or un-conventionally, we'll do what it's in our best interest.
You seem to forget a little thing called Tiananmen Square, in which a million demonstrators trying to overthrow the communists were left swinging in the wind by George H.W. Bush and "democratic' Europe for the sake of the mushrooming Chinese economy which has ironically been used to build the weapons that could destroy our nation. This would be the same Chinese economy which fueled the technology programs that manufactured the medium-range missile techonology which they sold to Iran, with extra special thanks to Bill Clinton. If we weren't going to fight for democracy when it had a legitimate shot at removing the communists in 1987 - when their army was a backwards, pissant operation, we're not going to do it with Taiwan now.