I've used US data only because I cannot find a poll in quite the same terms in Australia. According to the Washington Post at end of June:
The survey also suggests that the fog of war extended far beyond the Iraq battlefield. About one in four Americans incorrectly believes Iraq used chemical or biological weapons against U.S. forces during the conflict. Slightly more than six in 10 said Iraq had not, while the remainder weren't sure.
We can assume there would be few if any citizens who believed the nonfact of WMD use and opposed the war. The same article cites US support for the war at 67%. If you subtracted the 25% whose decision is grounded on a nonfact then the level of popular support starts looking fairly shaky.
The dramatic dip in Bush's numbers and in Blair's suggests that popular support was never all that deep and can be expected to continue eroding quite dramatically in light of the collapsing and contradictory stories coming out of Canberra, London and Washington. Sometime soon, for example, someone in the tradmedia is going to ask why Blair has not shared with Bush the slamdunk Niger vidence he claims to possess.