Realistically, there is zero chance the invasion would have happened without exaclty that trio of President, Sec-State & VP, plus or minus a Wolfowitz.
But the Republicans successfully goaded some Democrats into voting for it by threatening to taunt them. The US public needed some more important foreign blood to be spilled than Afghani. And that's the way the cookie crumbled...
Really? Wow, voting for a war you (allegedly) know to be wrong because you're worried about being "taunted". That's the most pathetic spineless thing I've ever heard. Worse than unashamed pro-war crowd, in some ways.
What happened to all those cowardly losers anyway? They all get voted out and replaced with people who were happy to continue those occupations and support the new wars and interventions during the Obama administration?
More generally, that would be a dereliction of duty too. The entire point of these checks and balances is so that an individual branch does not need to be trusted to make a wise choice.
I really don't see how you can reach that conclusion that prime mover on the Iraq invasion was the US public at large.
I thought Richard Clarke's book a few years later was pretty informative. Iirc, in his telling, they wanted to attack Iraq before 9/11 happened, and when it did happen, many in the administration didn't care at all who did it, they just wanted Iraq to pay. There was a line attributed to Rumsfeld "but Iraq has better targets".