I think you are remembering it wrong. The populace was pretty whipped up over 9-11, and running through the Taliban hadn't really satiated that. Also, in the era immediately after 9-11 there was a TON of second guessing of the way we had handled foreign policy up to that point with respect to fundamentalist Islamist terrorists, and how we had basically turned a blind eye to ever increasing provocations and attacks until if finally blew up on our doorstep. In that environment, even though Saddam was hardly a fundamentalist (more of a dictator who used religion when it was convenient) he HAD been extremely provocative, had used WMD's of the chemical variety in past, had invaded his neighbors, had sponsored terror (especially against Israel), was in breach of almost 20 UN resolutions, had allegedly participated in a plot to assassinate Bush Sr, and was actively stoking the rumors that he was close to or already had nuclear weaponry, at least of the dirty bomb variety (more in a gambit to enhance his position in the Middle East, but we didn't know that at the time). With the sting of 9-11 still so fresh and the feeling that we had missed so many signs and opportunities to prevent it, doing nothing about Saddam was not something people were interested in. No doubt the administration was hot to get into Iraq, but I do believe that they really thought they were doing so to prevent another 9-11 down the road. We had pretty much ignored Bin Laden, and he managed to orchestrate the largest foreign attack on US soil in our country's history...how could we ignore Hussein, who virtually EVERYBODY was saying was imminently acquiring nuclear weapons, and who had on many occasions vowed to use them against us and our allies?
The notion that the country, the congress, or almost anybody else was dragged into the Iraq War is just completely detached from reality. There were some anti-war folks out there for sure, and some not-necessarily anti-war but cooler heads advocating for caution or avoidance completely....but they were far and away the minority. There was absolutely no months of convincing required for the vast majority of the public. We did dance with Saddam for quite a while and gave him multiple opportunities to deescalate the situation from his end (whether or not he was really in a position to do that, or if we were being sincere in that effort is another debate), but that was to an entirely different purpose of cementing our legal case for the war to come both home and abroad...not to sway public opinion. That was already in the bag.
