That’s a loose thought process. If not Iraq, the media would have gotten Bush another way. Iraq was 5-6 years old before Bush really lost his footing. Events like Katrina and Valerie Plame were the hot issues that got public opinion over the edge....’culture of corruption’, etc. that was the central them in 2006. Additionally, if health care wasn’t passed in 2010, it would have been at some point in the next decade when they had the opening.
The GOP lost the Congress in 2006 because of three corrupt Congressmen and a string of bad GOP Senate candidates.
Couple that with the compliant media, and you got Obamacare. The Iraq War had little to do with it.
But leaving health care out of the picture, the GOP got into such straits because of the "double whammy." It wasn't just the economy (and the deficits and Katrina) that turned a lot of people against Bush. If the high-profile Obamacons of 2008 are any indication, Iraq was as important.
You could argue that Bush's listlessness and inability to speak up for his policies had more to do with the economic crisis, and that the slump was more important to the average citizen, but for some traditional Republican voters Iraq was where the disaffection started.