With less than two weeks left before Election Day, a big question is looming over the campaign for the White House, and it has nothing to do with the economy or the barrage of attacks between former President Donald J. Trump and Vice President Kamala Harris over judgment, character and mental fitness.

It is gender.

The issue is rarely directly addressed by either of the candidates. Yet the matter of Ms. Harris’s gender — and her potential to make history as the country’s first female president — is defining the campaign, creating a contest that is, in ways overt and subtle, a referendum on the role of women in American life.

Pro-Harris stickers plastered on bathroom stalls offer reminders, “woman to woman,” that their vote is private. Trump aides use sexualized epithets to deride liberal men as weak and effeminate. In poll after poll, a difference in voting patterns based on gender pervades every demographic group.

And in quiet conversations, some female Harris supporters can’t shake the uneasy feeling that men in their lives are struggling to support a woman — especially a Black and South Asian woman — even if they don’t want to admit it.

“If she were a man, would this race be this close?” Gov. Janet Mills of Maine asked a clutch of Democratic women after campaigning for Ms. Harris in suburban Pittsburgh. Joyce Reinoso, one of those women, shot back, “Oh, she would’ve won three weeks ago.”

Those who have studied voting patterns for decades say they have never before seen a presidential race where gender is so central to the electoral prospects of each candidate — even in 2016, when Hillary Clinton became the first woman to capture a major party nomination. They cite a series of factors: Mr. Trump’s well-documented denigration of women, Ms. Harris’s barrier-breaking potential, longstanding sexist views about women in power and, perhaps most centrally, the Supreme Court’s overturning of a constitutional right to abortion two years ago.