Start Change and MyDD just commissioned a 23 question national poll covering a variety of questions of national import. And they posed two on the subject of Iraq.
Question #12 is, did you support the invasion. Not how are things going or is it time to go. But did you support it at the time.
The results aren't surprising: strongly support 18.7%, support 28.7%, oppose 21.8%, strongly oppose 25.0%.
But they followed with an open-ended, why?
You can see the data here. But the thumbnail version is that there's no consensus for why people supported or opposed.
Some of this is a matter of the fuzziness built into an open-ended question. For instance, among supporters, 3% said they supported because it was "the right thing to do." 3.3% said that it was "inevitable/ [or] someone had to do something." Presumably these are different flavors of the same answer, though precisely how it answers the question, I'm not entirely sure.
Basically, what I draw from this is that every conceivable theory and ground of opposition to the war at least clocks in with a few percentage points of support. But no single reason registers even as much as ten percent.
At a deeper level, I suspect that there are more gut-level roots to both positions, ones that don't sound reasoned enough to state in their purest form. People then articulate those views from the various arguments on offer.