Admittedly, this is the kind of counterfactual that's impossible to prove, but my guess is that if she had voted against the war Clinton would be the Democratic candidate. Given the closeness of the race, her inherent advantages going in, and that the war had to be a liability it's hard to imagine that she wouldn't have prevailed without the Iraq albatross. Whether or not Clinton's support was sincere — I don't think it really matters — sometimes getting big policies wrong really is politically damaging.
I agree. Barack Obama is highly likely to be the next president of the United States because he opposed a dumb war. Democrats should take notice.