I don't think this claim holds up to the evidence. Looking at opinion polls between 9/11 and 2003's invasion of Iraq makes it unclear that a "very large majority" was against the invasion. Here's a quickly-found Gallup poll[0] from October 2002 wherein 53% of polled Americans supported a ground invasion of Iraq.
The American people were misled by government claims about WMDs and handwavy connections between Iraq and 9/11. But that doesn't permit us to retroactively declare that "well, if only the people knew in 2002 what we know now then they would have been against it."
[0] https://web.archive.org/web/20171201030755/http://news.gallu...