It didn't take years of little progress for the US public to become pessimistic about the Iraq War. The war had less than 50% approval only a year after starting. Also, contrary to what is commonly passed around as fact today, it was not abundantly clear that the Iraqi chemical weapons program no longer existed, as the US was never actually supplied with evidence that the Iraqi Biological Weapons program was done away with after the Gulf War, which is why it wasn't just the possible existence of WMDs that was given as justification, but the non-cooperation with inspectors also. In the early 2000s, soldiers were given multiple rounds of anthrax vaccine shots due to this lack of clarity. This is not to say that this justification a good reason, but it wasn't a clear lie at the time either, despite being repeated commonly as such on the internet these days.

https://www.nytimes.com/2004/04/29/us/the-2004-campaign-the-...