The New York Times asks the question as part of their regular poll with CBS, having just run a front-page editorial to fulminate on the subject. Now 'assault weapon' isn't a real category based on function, but a scary name invented to make the guns easier to ban during the Clinton Administration. We all remember the Clinton-era ban, and that it was allowed to sunset after ten years because it accomplished nothing whatsoever. Even the Brady folks couldn't muster anything positive to say about it.
Given that the name was invented for the sole purpose of being scary enough to sell gun control, the poll has always before found that a majority of respondents agreed to ban such guns. Not this time. The highest opposition on record for the poll was 34%. Now a clean majority oppose such bans.