In the wee hours of Monday morning, Elon Musk, the billionaire who has put nearly $120 million behind an effort to get Donald J. Trump elected, issued a simple warning on the social media platform he owns. “Men must vote!” he wrote at 2:43 a.m.
His post, a plea that has been issued by several Trump allies in the campaign’s final stretch, reflected a growing concern from Mr. Trump’s team that heavy turnout among women in several key battleground states could spell trouble on Election Day.
Polls have shown a large gender gap between Mr. Trump and Vice President Kamala Harris this year. Across the seven battleground states both campaigns view as critical to their victories, Ms. Harris dominates among women and Mr. Trump among men.
Women generally vote at a higher rate than men, and they have outpaced men in the turnout for early voting, a fact lamented last week by Charlie Kirk, the conservative leader of Turning Point Action, a political organization that has picked up much of the Trump campaign’s ground-game operation in battleground states.
“Early vote has been disproportionately female,” he wrote in a social media post. Like Mr. Musk, he ended with an exhortation: “Men need to GO VOTE NOW.”
The Harris campaign believes that women, energized by abortion rights in the wake of the Supreme Court’s decision to overturn Roe v. Wade, can help lift Ms. Harris to the presidency.
The Trump campaign has tried publicly to downplay such concerns, arguing that women are motivated by their concerns over the economy, a top issue for voters and one in which the Trump campaign believes it holds an advantage. Faced with early voting data, some Trump advisers have pointed to other trends, including higher turnout in rural areas, where both male and female voters are believed to lean toward Mr. Trump.
But in the waning days of the election, Mr. Trump has made a number of statements that have threatened to draw attention to his history of misogynistic remarks and behavior and his role in appointing the Supreme Court justices whose votes were crucial to overturning the constitutional right to an abortion.
Mr. Trump last week promised to be a protector of women “whether they like it or not,” after telling a crowd in Wisconsin that his advisers had told him to stop using a frequent line about his desire to protect women. He said in recent days that he would allow Robert F. Kennedy Jr., a vaccine skeptic whose views on abortion restrictions shifted several times during his failed presidential bid, to work on “women’s health.”
And his reaction to remarks shouted by people in his crowds has drawn attention to the sexist atmosphere of his events. Over the weekend, he laughed at a male rallygoer’s crude joke suggesting Ms. Harris had been a prostitute. On Monday, he seemed to approve of another remark from the crowd about Ms. Harris being put in a ring with the boxer Mike Tyson.
In Reading, Pa., Mr. Trump was telling an off-topic aside about Mr. Tyson when a man in the crowd yelled out. Mr. Trump said: “Oh, he says, ‘Put Mike in the ring with Kamala.’ That will be interesting.” The crowd roared and cheered.
The former president has shown signs that he is trying to appeal to women in his closing message. In North Carolina over the weekend, he targeted his fear-based appeal around crime and immigration, saying women “have to be protected where they’re at home in suburbia.”
And at some of his final rallies, the Trump campaign has been positioning more women in seats behind the stage, making sure that they are in the background of photographs and videos.
Though the arena was half-full at Mr. Trump’s rally in Reading, Pa., on Monday, the section directly behind him was stacked with women. As he spoke, they waved bright pink “Women for Trump” campaign signs in unison.
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