Despite Donald Trump’s repeated denials of nefarious behavior toward women and his media-blaming tactics, a new ABC/Washington Post poll shows that nearly 7 in 10 voters think Trump probably did make unwanted advances on women.

Nearly half ― 48 percent ― of Republicans agree. Only 23 percent say Trump probably hasn’t made unwanted advances on women, and 29 percent don’t have an opinion. Among independents, 71 percent think he has made such advances and 13 percent disagree. Not surprisingly, 87 percent of Democrats believe Trump probably followed through on his words captured in the 2005 discussion caught on tape with Billy Bush.

A majority of registered voters think that conversation goes beyond “locker room talk.” Fifty-two percent say the comments go farther than how most men talk about women, and 57 percent doubt the sincerity of Trump’s apology.

At the same time, most say the tape itself doesn’t make them less likely to vote for Trump. Presumably for Democrats that’s because they were already not voting for him, and for Republicans because they don’t want to see a Democrat win the presidency.

Trump has attempted to deflect the controversy by reminding Americans of Bill Clinton’s checkered past with women and Democratic nominee Hillary Clinton’s words related to those cases. But only 30 percent of voters think it’s a legitimate issue for this campaign. And just 13 percent say it’s a very or extremely important issue. Fifty-five percent say Trump’s treatment of women is a legitimate issue, including 36 percent who say it’s very or extremely important.

Voters in battleground states mirror these nationwide numbers. A CBS Battleground Tracker, which polls voters across 13 critical states, asked similar questions.

Seventy percent of voters in these states say Donald Trump doesn’t respect women ― including 66 percent of men. Fifty-seven percent say Trump’s comments on the tape were offensive, including 60 percent of independents and 70 percent of women.

Nearly half of battleground state voters ― including 40 percent of Republicans ― said the comments were offensive but didn’t change their vote intention. Only 5 percent of Republicans and 12 percent of independents said they couldn’t support Trump after hearing the tape. That indicates the effect of the tape could be limited.

But the effects of the sexual assault allegations that emerged late in the week aren’t included in these polls, which were conducted Oct. 10-13 (ABC/Washington Post) and Oct. 12-14 (CBS). And even small changes in voters’ willingness to vote for Trump could destroy his chances of winning the presidency, which were already very low.

Trump, of course, blames the media and falsely claims the polls are “close.” They’re not.

Polls close, but can you believe I lost large numbers of women voters based on made up events THAT NEVER HAPPENED. Media rigging election! — Donald J. Trump (@realDonaldTrump) October 16, 2016

Editor’s note: Donald Trump regularly incites political violence and is a serial liar, rampant xenophobe, racist, misogynist and birther who has repeatedly pledged to ban all Muslims — 1.6 billion members of an entire religion — from entering the U.S.