In light of gun sales and issuance of licences and permits it's probably higher than that. I suspect that people are simply not telling pollsters the truth.
And the issue is that your side simply assumes that what it wants is "common sense".
Which means that people that have never shot a gun and know nothing about them or how they work position themselves as knowing what is reasonable and common sense.
"Assault weapon" bans target certain kinds of rifles, shotguns, and handguns based on arbitrary features. Different people pick different arbitrary features to define "assault weapon" so there's not even a generally-accepted definition.
And you in particular don't seem to be interested in debating what should or shouldn't be allowed; I have no idea as to the depth of your knowledge but I have the distinct impression you consider yourself well informed and thus resistant to further education.
Since "assault weapons" are widely owned by regular people, your assertion that only criminals and the mentally ill would be targeted by banning them (per the "common sense" assumption) is a trolling insult on huge swathes of people.
Never mind that "only" 32% is a far larger minority than: blacks, Jews, Muslims, gays, transgendered people, Asians, atheists, lefties, or minimum-wage workers.