The biggest overlap between the Taiwan and Ukraine theaters of operations involves demands on logistics and on intelligence. To be sure, the US has kept a close watch on Chinese activity since the beginning of Russia’s invasion of Ukraine, but some of the electronic, cyber, and analytical assets currently devoted to helping Ukraine fight would undoubtedly need to be shifted towards China. Some of this effort could be replaced by the Europeans, but the US has enough sufficiently unique assets in this area that Ukraine would undoubtedly notice the shift.
In terms of logistics, the fight in Ukraine has already put a strain on the US defense industrial base. Fighting has used up stocks of weapons and ammunition as the course of fighting has turned towards attrition. Again, the US is fortunate that there’s not a lot of overlap between the operational demands in Ukraine and Taiwan, but US forces would likely suffer some shortages in the case of extended fighting on both sides of Eurasia. As noted, Taiwan is likely to take precedence if there’s competition between the two theaters.
The US has paid for the luxury to build a military sufficient to fight in both Asia and Europe, and not generally with the same weapons. There is undoubtedly some overlap in terms of air capabilities and logistical assets, but the immense fighting power of the US armed forces would not be inordinately strained by the need to wage war in both theaters because the theaters made different demands. Even if the war in Ukraine escalated to direct conflict between NATO and Russia, it is likely that the fighting would involve the fielded forces of European countries, with the United States playing an important support role. In short, the United States can fight both Russia and China at once… for a while, and with the help of some friends.