For the United States to actually declare war, it needs to be declared by the President and ultimately approved by US Congress. As far as the United States sending forces to intervene militarily, the President already has his approval thanks to the TRA. If the President was to engage in a full-on war with the People’s Republic of China, he’d probably need approval… but anything short-term and limited is entirely his option.
I don’t think anyone’s suggested that the United States, or the American president, “can’t” defend Taiwan. I think the belief amongst some is that, under some circumstance, the United States won’t defend Taiwan… the US will choose not to intervene.
I’m sure any US president will think twice/three/four times before sending more American soldiers to die in east Asia, especially if it isn’t obvious American interests are at risk, especially if American soldiers are deployed in Iraq + Iran + Afghanistan, especially if the rest of Asia (including traditional American allies) are calling for restraint.
No American soldier is legally or morally obligated to die for the cause of Taiwanese independence. Thomas Jefferson said “the tree of liberty must be refreshed from time to time with the blood of patriots and tyrants”… but that doesn’t mean the Taiwanese tree of liberty must be refreshed with American blood.