It's not impossible but I doubt they would be able to achieve the widespread support they had with the Kuwait war. You don't need to think about Kuwait even, the Korean War also saw UN forces fight against North Korea, China, and the Soviet Union. It wasn't just US troops fighting on Korea.
In the case of Taiwan, like I said, I doubt you would see a broad coalition like what happened in the first Gulf War. You might see something similar to what happened in the second Gulf War I think. But I think it would be pretty much impossible for the US to do war with China on their own turf. It is a lot more likely they would impose massive sanctions on China and attempt to blockade it rather than an actual war.