That's exactly right. They all signed the authorization for use of force and they were all right behind Clinton with his tough talk on Iraq. Then as soon as the protesters hit the streets and they realized their base was swinging into an anti-war movement, they all turned tail and ran for political cover. They needed a way to explain their vote on going to war so the whole "Bush lied" spin was wound up. The media latched onto it as it wound anything that even smells of scandal in the White House and the rest is (rewritten) history. It's disgusting.
Your post is a good summary of events. The Democrats' contention that they were manipulated makes them look like idiots.