So would another attack on US soil in the scale of 9-11 galvanise and unify the American people...
You mean like the attacks on 9-11 galvanized and unified them against Osama, Al Qaeda, and the Taliban...
...or demoralise and weaken our fighting will?
...or do you mean like how finding out they were suckered into a war that wasn't justified against an enemy that posed no threat to us, and being bogged down there for almost five years now, has demoralized them?
I think if there is another attack on Americans, and the government can prove who did it, the people would be more than willing to strike back and do whatever it took to avenge the attack. However, I think they will be more leery of just jumping in feet first whenever the government says there is an impending threat. By foolishly leading the people into the Iraq war, the government has shown the people they have to require more proof than simple scaremongering.