(The New York Times)

Vice President Kamala Harris will travel to the symbolic birthplace of the Republican Party to appear with Ms. Cheney, the highest-profile Republican to endorse her.

The appearance, with the most prominent Republican to cross party lines and endorse Ms. Harris, is part of Ms. Harris’s strategy to appeal to Republicans who are repelled by former President Donald J. Trump and his brand of politics.

Her stop with Ms. Cheney will follow Mr. Trump’s afternoon rally in Saginaw, Mich., a swing county in another battleground state that Democrats won in 2020. Recent polls have shown Ms. Harris gaining a narrow lead in Michigan, but the race is close and the state’s 15 electoral votes are still up for grabs in November. Ms. Harris travels to the state at the end of the day.

The candidates for vice president, Senator JD Vance of Ohio and Gov. Tim Walz of Minnesota, spent visiting swing states as they tried to capitalise on their performances in what might have been the last debate before Election Day. Ms. Harris toured hurricane-ravaged Augusta, Ga., and pledged that the federal government would cover the cleanup costs.

Donald J. Trump’s presidential campaign has aired a 30-second ad on television stations in Arizona, Georgia, North Carolina, Pennsylvania and Wisconsin this week at a cost, so far, of more than $450,000, according to AdImpact.

Like most Trump campaign ads, this one opens with a stern-looking photo of Vice President Kamala Harris. Bold text appears on the screen beside her.

“Harris is seeking to significantly raise taxes,” reads the male narrator, underscored by ominous-sounding music.

The ad closes by contrasting Ms. Harris unfavourably with her opponent. The tone of the music shifts from ominous to triumphant. Video shows Mr. Trump purposefully striding through a corridor in the Capitol as president, wearing a hard hat, touring a factory floor and shaking hands with fast-food workers. The narrator cites three of the most populist tax proposals from Mr. Trump’s 2024 campaign: “No taxes on tips, overtime or Social Security.”