In mid-October, Vice President JD Vance came face to face with a young woman who told him that he got her vote when she cast her first ballot as a U.S. citizen. At a town hall in Michigan, she asked why he was scapegoating immigrants for the issues he had vowed to solve as vice president.

Mr. Vance responded that his goal was not to “dehumanize” immigrants.

“To the extent that my rhetoric has been imperfect here, that’s on me,” Mr. Vance said.

But days later, when a heckler interrupted his speech with shouts of “Release the Epstein files” and “God bless our children,” Mr. Vance claimed without evidence that the man was an illegal immigrant.

And last week, at a rally in Michigan, Mr. Vance suggested that Dr. Abdul El-Sayed, a Muslim American and Democrat who is running in a tight race for the Senate, would lead an uprising similar to the unrest taking place in France.

“We have to understand what happens when our nation gives in to these kinds of people, to young men with zero attachment to its land or to its history,” Mr. Vance said of Dr. El-Sayed, who was born in the United States.

“Because what we saw in France,” he added, “the hatred, the ingratitude, the desire to destroy rather than the desire to build, that exact same cancer is what has corrupted Abdul El-Sayed writ large.”

As he has sought to rally support for G.O.P. candidates before the midterm elections, Mr. Vance has repeatedly reverted to deeply personal attacks and inflammatory rhetoric, playing a leading role in a campaign in which Republicans in tightening races have adopted xenophobic, anti-immigrant and anti-Muslim rhetoric.

He fat-shamed critics, and suggested that the Democratic Senate candidate in Texas was gay and had inappropriate relationships with children. He asserted that a Black Democratic candidate in Florida did not belong in the United States because of her socialist views. He questioned the Christianity of a Kansas pastor running for Senate. And he defended a widely criticized ad featuring the estranged mother of the Democrat running for governor in Ohio, Dr. Amy Acton. Dr. Acton has not spoken to her since her mother’s husband was charged with raping Dr. Acton when she was 12.

Vice presidents have historically been called on to be rhetorical attack dogs, particularly during campaign seasons, and Mr. Vance is second-in-command to a president whose go-to defense is often aggression and insults.

But Mr. Vance’s sharp-edged rhetoric is revealing of his political instincts on the eve of the next major campaign, as attention shifts to the 2028 race for the White House and his potential candidacy to succeed President Trump.

“His political juice is still very much open to question, and Vance has put a lot of his credibility on the line in the places he visited,” said Matthew Dallek, a political historian at George Washington University. “He’s looking for ways to say to his base voters that ‘I should be the one to inherit the Trump mantle. I can go where Trump also goes, and go to depths that Trump hasn’t even visited yet.’”

In response to a request for comment, Luke Schroeder, a spokesman for Mr. Vance, said in a statement that The New York Times was “cherry-picking his comments to manufacture a politically convenient caricature.”

“The vice president’s message is simple: America belongs to those of all colors and creeds who love it, not to those who hate it,” he added. “The vice president has rightly held radical Democrats accountable for their apparent contempt for the American way of life.”

Mr. Vance has demurred when asked whether he plans to run in 2028. “My wife will tell you this: I’m a procrastinator. I hate thinking about it,” he said at a recent CBS News town hall, adding, “Anything could happen, man.”

The president has so far declined to name Mr. Vance as his heir apparent. In the closing stretch of the midterm elections, he has privately questioned why Mr. Vance has not drawn bigger crowds at the rallies he has headlined.