In short, they embraced Mr. Trump’s sales pitch for himself.

“I think that women see the big picture — women are smart,” Mrs. Gauta said. “The fact that he said something crude,” she said “is not going to change my mind about the good he can do for our country.

“Did I like that, no,” she went on. “But do I think he can do a better job than Hillary? Absolutely. I think he has got the best interests of this country at heart. He’s got a beautiful family; he wants to leave a nice country — the great country he was raised in — for his kids. And I think he said the only way I’m going to get that done is by being president myself.”

She took her sons, 14 and 16, to a Trump rally, and said she “was even more impressed by him in person than on TV.” But as to his sometimes foul mouth, “If my boys ever said anything like that, I’d put them over my knee and spank them.’’

In Chicago, Nicole Been, 22, a Roman Catholic who attends DePaul University, is deeply opposed to abortion and the “hookup culture.” She complained that other students branded her a racist and a bigot for supporting Mr. Trump.

In Philadelphia, Daphne Goggins, 53, an African-American community activist and ardent Republican, always knew she would vote for Mr. Trump. She said she believed decades of Democratic efforts had done little for black people. When Mr. Trump invited her to a minority outreach meeting, she told him tearfully that “for the first time in my life, I feel like my vote is going to count.” (Only 4 percent of black women, exit polls show, supported Mr. Trump, while 26 percent of Latinas did.)

For the women interviewed, as for male Trump backers, the economy was of utmost concern. Mrs. Gauta and her husband are tired of paying $1,800 a month in health care premiums, with a $12,000 annual deductible. Ms. Lincoln, the retired college administrator, now works at her husband’s auto body shop in Old Town, Me., to help pay the bills.