Vice President Kamala Harris took her message from campaign-speak to conversational during an interview with the late-night host Stephen Colbert on Tuesday night, as she acknowledged fading hopes for a cease-fire in Gaza while keeping up her attacks on former President Donald J. Trump for his relationship with Vladimir V. Putin of Russia.

As if to underscore her growing confidence — after a three-day stretch in which Ms. Harris appeared in her most extended series of interviews of the campaign — she joined Mr. Colbert in cracking open a can of Miller High Life in front of his CBS studio audience in Manhattan.

“The champagne of beers,” Ms. Harris joked, after Mr. Colbert noted that she had requested that brand of suds — which is brewed in the battleground state of Wisconsin.

During her taped appearance on “The Late Show,” Ms. Harris also dealt with far weightier subjects. Asked about the war in Gaza, an issue that could threaten her chances of winning states like Michigan, she suggested the conflict was unlikely to end soon, even as she urged optimism.

“We cannot lose some belief in the possibility” of a cease-fire, she said, adding that “the United States must work and not lose hope and not throw up our hands.”

And she condemned Mr. Trump — for the second time on Tuesday — over reporting from a new book by the journalist Bob Woodward that claimed that Mr. Trump had sent rare Covid test machines to Mr. Putin in the early days of the pandemic.

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