Here we see all the merit of soft power (threats, words) versus hard power (attacking, invading, occupying) when we realize what the limits are. So does the other side, BTW. But not using hard power also lets the other side in the uncertainty of what would happen, and it also costs much less in human lives.
Belonging to the axis of weasel, several arguments come to mind.

First, the US president used an argument (that could have been accepted) about the WMD threat but it was a lie or at least misleading.

Second, he used another argument (Saddam being dangerous) that was illegal as international law does not recognize this as a motive for war and the UN didn't agree with this argument either.

Third, the US is stuck in Iraq for who know how long and countries that didn't agree with the war are not going to get trapped the same way.

Fourth, any other country participating in the war won't be able to send as many troops or equipment as the US and this means the support won't be practical but only political. It won't make any difference in the final outcome anyway. Bush has been rather insulting to the rest of the world (if you're not for us, you're against us), so expecting political help....

Fifth, the fight against terrorism is already done in international cooperation and the axis of weasel's troops are in Afghanistan.

Sixth, it's all very nice to ridicule other countries when not personally involved in a war halfway around the globe, but comfortably sitting in front of his PC.

Raoul