Some of Mr. Trump’s female backers initially supported him only reluctantly or do so now in spite of reservations about his bawdy language and erratic behavior. But they shared in his victory after the bitter and partisan battle over the confirmation of Justice Brett M. Kavanaugh. And many believe the president when he reminds them during each of his hourlong pep rallies that the world they know — largely Christian, conservative and white — is at stake on Tuesday.

“Honestly, I’m nervous about it,” Amy Kremer, a Tea Party activist and the co-founder of the Women for Trump PAC, said of the election, which is widely viewed as a referendum on Mr. Trump. “I’ve never seen this energy and momentum for a midterm, but also the polls weren’t correct in 2016.”

Ms. Kremer said she and the other women in her Atlanta-area social circle “love” Mr. Trump, adding, “We like when somebody promises to do something and they follow through on it.”

But that warmth toward the president is decidedly a minority view among women around the country, and Republican officials fret privately that Mr. Trump’s harder-edged messages will alienate the women the party needs to preserve vital seats.