Universal basic income was Andrew Yang’s signature issue in his 2020 presidential run, and it will be a centerpiece of his New York City mayoral campaign, which he officially began Wednesday night with a launch video.

But during the months Mr. Yang spent contemplating a run for mayor, his competitors preemptively made his issue their own.

Carlos Menchaca, a progressive city councilman, is planning to introduce legislation that would create a targeted universal basic income program in New York City. Eric Adams, Brooklyn’s more centrist borough president, wants to explore universal basic income, too. So does Dianne Morales, a former nonprofit executive running to the far left.

In a race of more than a dozen Democratic candidates, with many trying to out-progressive one another, pushing for a guaranteed income program could be viewed as a form of virtue signaling to the left.

But it also shows how an issue that was Mr. Yang’s signature talking point on the 2020 campaign trail has gained enough acceptance to be co-opted by other candidates — a development that threatens to undermine Mr. Yang’s central argument for running.

The candidates’ embrace of guaranteed income doesn’t mean that a broad-based program is a particularly viable idea for New York City, given the battering its economy has taken in the pandemic, its yawning budgetary needs and the amount of money needed to guarantee income to the city’s adult population of roughly 6.6 million.

Mr. Yang acknowledged as much in his campaign rollout. His proposal for the “largest basic income program in the country” is by no means universal. He would target annual cash payments of about $2,000 to a half million of the poorest New Yorkers, in a city of 8.4 million.

Mr. Yang said his proposal would cost the city $1 billion a year — a daunting sum given that the city faces budget deficits in the billions of dollars in coming years. He says further expansion of the program would be dependent upon “more funding from public and philanthropic organizations, with the vision of eventually ending poverty in New York City altogether.”

His plan for the country was more far-reaching: He had envisioned giving every American citizen over 18 years of age $1,000 a month in guaranteed federal income, or $12,000 a year, a no-strings-attached dispensation he said was made necessary by the increasingly widespread automation of jobs.

“I’m identified with universal basic income for a reason,” he said in a recent interview. “I think it’s the most direct and effective thing we could do to improve the lives of tens of millions of Americans who are struggling right now, and anything I do in public life will be advancing the goal of eradicating poverty in our society.”

In the interview, Mr. Yang swatted away the notion that his future opponents were trying to steal his signature issue from him. He adopted a more-the-merrier posture.

“Frankly, any mayoral candidate who is not making it part of their platform is missing the boat,” Mr. Yang said.

Critics argue that a guaranteed income could discourage people from working. Still, the fact that several of the candidates vying to run the economic and cultural capital of the United States are exploring the notion of a guaranteed income does suggest that the concept has gained some momentum.

There are now guaranteed income demonstration projects underway in Jackson, Miss.; Santa Clara County, Calif.; and St. Paul, Minn. The terms “universal basic income” and “guaranteed income” are sometimes used interchangeably, but they differ. Many pilot programs are not universal but, like Mr. Yang’s proposal, instead would supply income only to the poorest members of society. Unlike many existing social assistance programs, they would not dictate how recipients spend the money.

Natalie Foster, a co-chair of the Economic Security Project, which advocates a guaranteed income, said she has had conversations with more than one New York City mayoral candidate on the topic.

“It’s exciting to see it being an issue in the race and not surprising at all, given the momentum across the country,” Ms. Foster said.

The other candidates touting universal basic income in the mayoral race are largely doing so in less specific terms.

Mr. Menchaca said he hopes to include a pilot program in this year’s budget that targets cash grants to low-income New Yorkers. The details of that program have yet to be hammered out.

In a recent radio interview, Ms. Morales called for a “universal basic income for people who need it,” and like Mr. Menchaca, suggested the question of how to fund it was something of a red herring, one that often gets asked “when we start talking about prioritizing the needs of the neediest New Yorkers.”

She said she would take a look at some of the city’s budgetary “bloating,” including at the New York Police Department, and expressed hope for state aid. In a subsequent email, her spokesman said Ms. Morales thinks a “local basic income” should be funded through a wealth and luxury tax on the “superrich that phases out and does not sacrifice the safety net.”

At a recent mayoral forum, Mr. Adams, the Brooklyn borough president, said universal basic income could be an important tool “to get people over this very difficult time, particularly low-income New Yorkers.”

Asked for specifics, a spokesman declined to provide further details.

Other candidates, including Scott M. Stringer, the city’s comptroller, and Kathryn Garcia, its former sanitation commissioner, said they would prefer to see some version of the idea implemented at the federal level instead.

Mr. Yang quit the presidential race in February after failing to gain ground in the New Hampshire primary, but he succeeded in making himself a political celebrity — and casting a klieg light on universal basic income. In various forms, the concept has been implemented in small pilot programs around the country, one of which his nonprofit organization, Humanity Forward, is helping to fund in the Columbia County city of Hudson, N.Y.

The general idea of a guaranteed income goes back centuries. Martin Luther King Jr. was a prominent, and early, proponent of the idea in the 20th century, and his son, Martin Luther King III, has continued pushing for it in his father’s stead.

“It’s really immoral for us to have people living on the streets in the United States,” said Mr. King, the co-chair of Mr. Yang’s campaign.

A new group, Mayors for a Guaranteed Income, is pushing for a federal guaranteed income and counts more than two dozen mayors as members, including Ras Baraka of Newark, N.J., Eric Garcetti of Los Angeles and Keisha Lance Bottoms of Atlanta.

By Ms. Foster’s count, there are more than 10 pieces of legislation in Congress that would guarantee an income for families until the current economic crisis is over.

“And that is political warp speed,” she said.

One of the most prominent universal basic income pilots in the United States — the first program spearheaded by a mayor — is now wrapping up in Stockton, Calif. Since February 2019, the privately funded program has given 125 Stockton residents $500 a month. Recipients like Tomas Vargas Jr. will receive their last payments on Jan. 15.

Before he joined the program, Mr. Vargas was working as a U.P.S. supervisor. The monthly checks gave him enough financial security and confidence to start looking for a better job. Now he works as a case manager at a Stockton nonprofit. Instead of living paycheck to paycheck and constantly looking for additional ways to make ends meet, he has time to read stories to his young children at bedtime.

The no-strings-attached approach is “the beauty” of the program, he said. “It treats you like a human.”