Depends on your definition of "win".
The US can reduce China to a glowing crater - at the price of being reduced to a glowing crater itself. That's probably not "win" in your book (nor in mine).
The US cannot conquer mainland China.
Can the US defeat an attempted mainland invasion of Taiwan? Maybe. The answer would be no if they shared a land border, but they don't. That 90 miles of water makes an invasion much more difficult and vulnerable. And China has no experience with amphibious assaults. The US would take losses in such a case, but would they win? I'm not sure anybody knows.
> Taiwan is idealogical to China. Taiwan is merely a pawn in the game for the US. The US will bow out of a war for Taiwan within years but China will never give up - even if the war lasts 100 years.
Taiwan is at least somewhat ideological for the US. We believe in the right of self-determination (going clear back to the Declaration of Independence), and we believe that Taiwan should have that right.
It's ideological for China because Xi made it so. I'm not an expert, but I don't think it was ideological for China under, say, Deng. Well, Xi won't live another 100 years. Will it still be ideological for the next guy?