Armed with a clipboard and campaign literature, Liz Minnella strolled through a neighborhood in New Hope, Pa., optimistic that by the end of her day of door-knocking, the small town would live up to its name for Vice President Kamala Harris’s campaign.

There wasn’t a political yard sign in sight, which Ms. Minnella, who had only recently become a Democratic activist, took to mean that she might find some persuadable voters. When a blonde woman in a Villanova sweatshirt answered one door with a broad smile, Ms. Minnella, a Villanova graduate, thought aloud, “This is my lady.”

The woman, a 52-year-old Republican, was eager to talk, even though Ms. Minnella’s voter list had highlighted her daughter, an independent. Ms. Minnella tried to steer the conversation toward reproductive rights, but it eventually circled back to the woman’s fears that migrants would bring violent crime to her wealthy Philadelphia suburb. The woman thanked Ms. Minnella for the “civil conversation,” but her mind was unchanged — she was voting for former President Donald J. Trump.

The episode reflected the obstacles that white women who support Ms. Harris are confronting as they try to persuade their ideologically diverse counterparts to join her cause, an effort that could potentially decide the election.

While much attention has focused on how Ms. Harris’s chances could be imperiled by groups like Black men — the second-most loyal Democratic voters after Black women — pollsters and strategists say the race is more likely to come down to white women.

They are the country’s largest voting demographic, making up about 30 percent of the electorate, and they consistently turn out at very high rates. They tend to swing in larger numbers toward the Republican in presidential elections — including in the last two contests for Mr. Trump.