Has the war been terribly handled PR wise, yes! (especially from 04 thru 06). It has been somewhat better of late.
With that said, the Iraq war (WOT) is not unpopular. Is the American public bored with it (for lack of a better term). Yes......But those who suggest they are against the war in Iraq....for the most part their stance is a mile wide and an inch deep.
Meaning, a coherent, educated discussion on the topic can make a large segment of the population understand the need to stay on the offensive in this WOT. That success in Iraq is vital to being successful in the WOT. The majority of the American public want that (and it's happening).
Fact is Iraq, the Dem's won't be talking about it nearly as much come Nov 08 (because of the clear success that will continue to be happening there).
However, I also think the situation is much worse than that. Most rational Americans have probably (rightly) concluded that this administration officially exposed the so-called "war on terror" as a complete fraud when it p!ssed away thousands of lives and billions of dollars on a military campaign in a Third World sh!t-hole while at the same time it was pushing for the establishment of legal status for millions of foreign invaders right here in the U.S.
THAT is what is ultimately going to destroy the GOP's presidential prospects in 2008.