March 31, 2016 6:52 AM EDT

Almost as much as wealth, Donald Trump regards women as a measure of success. He’s married to a former model, frequently recounts his history of romantic conquests and turned a recent presidential forum into a referendum on penis size. But whatever prowess he may have elsewhere, Trump has problems with women in the polls.

So much so that female voters are becoming an impediment to his shot at the White House. Trump’s divisive appeal has won over disaffected white male voters, who have carried him to pluralities in the crowded GOP primaries. But his swaggering style and oddball, offensive remarks have made him toxic to the women who swing general elections. Nearly three-quarters of women in a March 24 CNN poll said they had an unfavorable view of Trump. In a recent NBC/Wall Street Journal poll, nearly half of Republican women surveyed said they couldn’t imagine voting for the GOP front runner.

Trump’s dismal standing with women is the single biggest reason strategists in both parties predict his nomination would make Hillary Clinton the 45th U.S. President. Women have cast more votes than men in every general election since 1964 and voted at higher rates than men in every race since 1980. It’s very difficult for a candidate to win a general election if he’s underwater with the nation’s largest and most reliable voting bloc.

Republicans know from experience. They’ve lost women in every presidential race since 1988–a stretch during which they’ve carried the popular vote exactly once, in 2004. In 2012, Barack Obama won women by double digits after his allies painted Mitt Romney’s positions on abortion, contraception and the economy as part of a GOP “war on women.”

Trump is an easier target. In recent days alone, he has insulted the appearance of Senator Ted Cruz’s wife and questioned the integrity of a female reporter who pressed battery charges against his own campaign manager. Over the course of the campaign, he has called former GOP rival Carly Fiorina ugly and repeatedly attacked Fox News anchor Megyn Kelly. On March 30 he said women who have illegal abortions should face “some form of punishment.” If Trump wins the Republican nomination, “he’ll become a poster child for misogyny,” predicts Katie Packer, a former Romney strategist.

To recover, Trump will argue that he has hired “thousands” of women in his businesses, and he could opt to dispatch his daughter Ivanka to more public events. “Expect to see him deploy more female surrogates to make his case with women voters,” says Michele Swers, a political-science professor at Georgetown University. Otherwise, says Jennifer Lawless of American University’s Women & Politics Institute, it’s “virtually impossible to envision any scenario whereby 50% of female voters would cast their ballots for him.”

–ALEX ALTMAN AND JAY NEWTON-SMALL

This appears in the April 11, 2016 issue of TIME.

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Write to Alex Altman at alex_altman@timemagazine.com.

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