Wiki has a series of poll results on public opinion of Iraq during after the war. [1] In May 2003, 79% of Americans thought the war was justified, regardless of whether or not WMD existed. And by the time the war had kicked off 90% of Americans believed it "at least somewhat likely" that WMD would be found.
[1] - https://en.wikipedia.org/wiki/Public_opinion_in_the_United_S...
In the UK and AU, the two principal partners of the "coalition of the willing", few in the public felt the situation justified and the bulk of those with exposure to global policy, military intell, travel abroad etc. definitely felt it was a bogus war.
Tony Blair was all too aware the supporting intelligence was thin and inadequate at the time - which came out in followup Royal Commissions(?) (they had a big UK inquiry into the matter), and John Howard (AU) was happy to play along despite a lack of backing from ASIO et al on the intel as it was a treaty obligation for AU and not pushing back gave leverage for other US-AU deals.
Altogether it was much less a coalition of the willing than it was a tagging along of the bribed.
https://en.m.wikipedia.org/wiki/Protests_against_the_Iraq_Wa...
> According to the French academic Dominique Reynié, between January 3 and April 12, 2003, 36 million people across the globe took part in almost 3,000 protests against the Iraq war.
> In the United States, even though pro-war demonstrators have been quoted as referring to anti-war protests as a "vocal minority", Gallup Polls updated September 14, 2007 state, "Since the summer of 2005, opponents of the war have tended to outnumber supporters. A majority of Americans believe the war was a mistake."