The War on Terror is indeed fundamentally different from WWII, in that it must be sacrifice-free for 99% of Americans, or it won’t be fought at all.
Its fundamental difference is that in WWII the public was allowed to hate the "dirty Japs" and "Krauts," and the famous quote from Adm. Halsey, "KILL JAPS! KILL JAPS! KILL MORE JAPS! You will help to kill the yellow bastards if you do your job well," was considered a rallying cry. There was always the in-the-future desire to somehow morph Japan into a peace-loving nation (cf. Captain Cassidy's "skates" monologue in the 1943 movie Destination Tokyo), but in the meantime, the work at hand was to beat back and ultimately conquer Imperial Japan, by any means necessary. When we come to the same conclusion about militant Islamists, we will win, and the world will be a much better place.
Its not as different as you are thinking though.
Americans up till Dec 1941 were extremely isolationist and would have behaved similarly if Roosevelt declared war in say 1939, it was Pearl Harbor attack that changed Americans views.
Sure, we were attacked 9/11 by Al-Qaeda then later invaded Iraq, but if Truman had invaded Eastern Europe in 1945 starting a ground war with the USSR after Germany's surrendered it would have been as unpopular as Iraq turned out to be in 2006.
Now dropping those two Nukes on Japan was the cleanest and most popular option from the US standpoint.