Former President Donald Trump traded his signature suit jacket for a fast-food apron Sunday as he looked to expand his advantage over Kamala Harris with blue-collar workers who have flocked behind his presidential campaign.

The spectacle of Mr. Trump taking orders and working the fryer at McDonald’s attracted thousands of supporters, and the stage was selected so he could rehash his unproven claim that Ms. Harris lied when she said she worked at McDonald’s while in college.

“I’m going for a job right now at McDonald’s,” Mr. Trump told reporters after arriving in Pennsylvania. “I’ve really wanted to do this all my life, and now I’m going to do it because she didn’t do it.”

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Soon afterward, Mr. Trump, speaking through the drive-in window, said, “I’ve now worked for 15 minutes more than Kamala at McDonald’s.”

Harris campaign spokesman Ian Sams said that “when Trump feels desperate, all he knows how to do is lie.”

“He can’t understand what it’s like to have a summer job because he was handed millions on a silver platter, only to blow it,” Mr. Sams said.

The Democratic presidential nominee has said she worked at a McDonald’s while in college at Howard University in Washington. One family friend, Wanda Kagan, has told The New York Times in a contemporary interview that she remembers Ms. Harris working there.

No employment or other records confirm that she held the fast-food job, and no co-workers have publicly come forward with memories of working with the future vice president.

Mr. Trump reiterated that Ms. Harris cannot be trusted at a town hall event Sunday night in Lancaster.

He said Ms. Harris’ evolution on issues, including natural gas fracking and taxpayer-funded sex changes for prisoners, smacks of politics.

“She is only doing this because of the election,” Mr. Trump said.

Meanwhile, Ms. Harris, celebrating her 60th birthday, visited a pair of churches in Georgia as part of a “Souls to the Polls” push.

The effort focused on strengthening her hand with Black voters, who have been central to winning Democratic coalitions and must turn out in large numbers for Ms. Harris to win.

Team Harris is seeing warning signs.

Polls show that Mr. Trump has eaten into the massive advantage Democrats have traditionally held with Black and Hispanic voters, particularly among men.

At the New Birth Missionary Baptist Church in Stonecrest, Ms. Harris said the nation is at a “crossroads.”

“Where we go from here is up to us as Americans,” she said. “We face this question: What kind of country do we want to live in? A country of chaos, fear and hate, or a country of freedom, compassion and justice?”

Pastor Jamal Bryant directed his message at the men in the crowd.

“It takes a real man to support a real woman,” Mr. Bryant said. “When Black women roll up their sleeves, then society has got to change.”

Musician Stevie Wonder serenaded Ms. Harris for her birthday at her second stop, Divine Faith Ministries International in Jonesboro.

The Harris camp highlighted Mr. Trump’s appearance Sunday on Fox News “MediaBuzz,” where he denied knowing that fact-checkers had cast doubt on his claim that Haitian migrants were eating dogs and cats in Springfield, Ohio.

He defended his belief that the “enemy within” is more dangerous than foreign adversaries and that Jan. 6 was a “day of love.”

“This was a protest against a rigged election,” Mr. Trump said. “And I’ll tell you, there was a beauty to it, and there was a love to it that I’ve never seen before.”

Ammar Moussa, a Harris campaign spokesperson, said the responses show Mr. Trump “cannot help but show himself as the unhinged, angry, unstable man that he is.”

“This is precisely why his handlers are hiding him from major mainstream interviews and refusing to let him debate again,” Mr. Moussa said. “They don’t want the country to see this candidate in decline.”

On the campaign trail, Ms. Harris has questioned Mr. Trump’s mental fitness for the job and demanded that he release his medical records, following her lead and that of “every other presidential candidate in the modern era.”

At his town hall event, moderated by former ESPN anchor Sage Steele, Mr. Trump rejected the idea he was losing his mental fastball.

Mr. Trump highlighted a recent opinion piece in The Wall Street Journal that said the 78-year-old showed “no sign of such slippage” during a 90-minute editorial board meeting and “seems more confident and is certainly more knowledgeable about policy than he was in 2015.”

Mr. Trump assured the audience he has no cognitive problems.

“She may have a cognitive problem,” he said of Ms. Harris without elaborating.

At the meeting, Mr. Trump reiterated his commitment to ending the taxation of Social Security benefits, restaurant tips and overtime for all workers. He also promised to significantly expand oil and gas development to reduce energy costs and inflation.

He pledged to work to bring down interest rates on home loans, secure the southern border, and deport millions of illegal immigrants, starting with violent criminals.

“The Black population — over the last short period of time — their unemployment numbers have just skyrocketed,” he said. “The reason is the people coming into the country illegally are taking their jobs.”

Mr. Trump said it is “not financially feasible or sustainable” for taxpayers to have to cover the costs associated with the millions of illegal immigrants who have entered the country.

He also took a few seconds to wish Ms. Harris a happy birthday.

“By the way, it is her 60th birthday, so I want to wish her a happy 60th birthday,” he said, drawing murmurs and boos from his supporters.  “No, happy birthday and many more — and I mean it.”

Mr. Trump planned to travel to Pittsburgh on Sunday night to attend the National Football League game between the Steelers and the New York Jets.

Seeking to steal some of his thunder, the Harris campaign announced she had received endorsements from former Steelers stars, including Hall of Fame running back Jerome Bettis.