Vice President Kamala Harris campaigned for the presidency on the toughest immigration platform of any Democrat in decades: She vowed to continue the Biden administrations’s crackdown on asylum and to impose order on the southern border. She championed her record as a border-state prosecutor and her support of a bipartisan border bill that failed after former President Donald J. Trump urged Republicans to reject it.

But her message fell flat, as voters across the country doubted her resolve, associated her with the Biden administration’s failures at the border or were simply won over by Mr. Trump’s starkly xenophobic rhetoric.

His relentless portrayals of migrants crossing the southern border as an invading force, and Republicans’ false claims that Democrats were welcoming migrants into the country in hopes that they would vote for their party, effectively overwhelmed Ms. Harris’s milder attempts to neutralize the issue.

“I don’t think she had a message on immigration, and even if she did, I wouldn’t have believed it,” said Kathy Maranville, 70, a systems analyst in Waverly, Ga., who described herself as a conservative.

In the suburbs of Houston and Atlanta, Republicans denounced undocumented migrants who were charged in the killings of girls and young women. In blue cities and states like Chicago and Massachusetts, they cast newly arrived foreigners as a drain on schools, housing and hospitals.

“It was one of the issues that invoked an emotional response from voters,” said Ryan Williams, a Republican strategist and former spokesman and aide to Mitt Romney, who is now a Utah senator.