At first glance, this might seem like just the right moment for New York City’s deep-pocketed philanthropists to flex some muscle.

To hear Mayor Eric Adams tell it, the city is teetering on the edge of fiscal calamity, prompted largely by the costs of sheltering and feeding soaring numbers of migrants coming into the city. He has asked New York’s millionaires and billionaires to step in and help fill some of the budget holes that have prompted major cuts to schools, libraries, parks and the police.

But even under a mayor who has explicitly cast himself as a pro-business leader eager to work with philanthropists, wealthy New Yorkers accustomed to seeing returns on their investments and clear results from their giving are confronting the limits of how much their generosity can truly shape a struggling city.

Much of New York’s influential philanthropic class, which for years has harbored grand ambitions about how private money can influence public life, is newly wary of giving to causes aimed at addressing the city’s biggest problems, according to conversations with more than 20 donors, philanthropic advisers and fund-raisers. In some cases, donors are choosing instead to spend their money on uncontroversial local causes or on issues outside the city.

They worry that the city’s complex tangle of crises — migrants, homelessness, housing and the cost of living — cannot be easily fixed, even if philanthropists band together to help.

Donors who once found a unifying local cause in charter schools are reckoning with a political backlash and the reality that their boldest aspirations for improving education have not materialized. And some philanthropists who supported the city during the height of the coronavirus pandemic are now turning their focus to the presidential race and the Israel-Hamas war.

At the same time, donors — few of whom have strong connections to Mr. Adams and his inner circle — have noted the escalating questions about City Hall’s ability to manage the city’s many problems.

‘No hopeful message’

A recent fund-raising campaign to support asylum seekers offered a striking example.

The effort, which was a top priority last year for the Mayor’s Fund to Advance New York City, a city-run nonprofit that partners with donors, brought in less than $3 million in cash, alongside the equivalent of $2.7 million in in-kind donations, most of which was raised from philanthropic organizations rather than individual donors. Mr. Adams has said that providing services for migrants could cost the city as much as $12 billion over the next few years, unless the federal government intervenes.

There is a precedent for New York’s wealthiest to help ease migrants into the city. When waves of European immigrants started arriving in New York in the late 1800s, the city’s philanthropists banded together to create settlement houses, which provided social services and offered insights for the local government about how best to handle migrants. Many of these organizations are still influential in city life.

But today, “there’s no hopeful message here that people want to invest in,” said Grace Bonilla, who runs the charity United Way of New York City.

“It’s a hard conversation to have with donors when your mayor is saying, not only do we not have good solutions for a problem that should be solved by the federal government, and I agree with that, but we’re also cutting the budget,” she said.

Ms. Bonilla said there was a feeling of “giving exhaustion” still lingering from the pandemic, when philanthropists were able to see the tangible results of their donations. Even some wealthy New Yorkers who fled the city during the worst of the pandemic contributed handsomely to public emergency relief efforts, in some cases holding their noses to fund initiatives led by former Mayor Bill de Blasio, who was critical of what he considered the outsize role of private money in city politics.

The Mayor’s Fund raised over $77 million during the fiscal year that included the first half of 2020, its biggest haul since the last year of former Mayor Michael R. Bloomberg’s tenure. The fund raised just under $10 million, including some of the donations to the campaign to support migrants, during the first full fiscal year of Mr. Adams’s mayoralty, which was the lowest amount in at least a decade.

Philanthropists are not always keen to give directly to the government, said Kathryn S. Wylde, president of the Partnership for New York City, a business group that works with some of the city’s most prominent donors. Instead, they give to causes championed by people they trust, like Mr. Bloomberg, one of their own.

“Listen, this administration isn’t led by a billionaire,” Ms. Wylde said. “The Adams administration is starting from scratch in terms of developing their relationship with the philanthropic community.”

Kayla Mamelak, a spokeswoman for the mayor, said in a statement that the city needed “meaningful financial help” from the federal government.

“We are exceptionally grateful to our philanthropic partners who have stepped up to donate — not just to the Asylum Seeker Relief Fund, but to the several nonprofit and charity organizations we have directed donors toward — but, the reality is, New Yorkers should not have to bear the brunt of this crisis largely alone,” she said, noting that the relief fund listed nonprofits where New Yorkers could drop off donated goods.

No match for budget cuts

Donors have given generously over the past year to traditional causes like private hospitals and cultural institutions, including the newly opened, $500 million Perelman Performing Arts Center in Lower Manhattan, which was funded largely by a veritable who’s who of the city’s philanthropists, including Mr. Bloomberg, who contributed $130 million through his charity, Bloomberg Philanthropies.

But lately, even when donors do give to municipal causes, their money seems to be no match for the extent of the local budget cuts.

The New York Public Library raised $52 million in private donations during the fiscal year that ended in July. The library system, which receives more than half of its revenue from the city, is nonetheless suspending Sunday service at all of its branches following the city’s cuts to its library budget, and is preparing to further reduce service if the mayor enacts more cuts.

The Robin Hood Foundation, the anti-poverty group that has long been one of Wall Street’s preferred charities, has focused much of its recent advocacy on the city’s lack of affordable child care and announced $3 million in grants to the Mayor’s Fund last year to help families access care. That has not prevented the mayor from cutting hundreds of millions of dollars from the city’s popular prekindergarten program for 3-year-olds.

At the same time, some boldfaced names have focused their recent spending on supporting Israel amid its war with Hamas.

Mr. Bloomberg, who remains New York’s most influential philanthropist, recently put up nearly half of an $88 million contribution to Israel’s emergency medical service.

The UJA-Federation of New York, a Jewish charity, raised $45 million from local financiers at its recent annual gala, called the Wall Street Dinner, and another $75 million from “the Wall Street community” to support the federation’s emergency fund for Israel. Michael Cayre, a real estate developer and an owner of Casa Cipriani, helped organize a gala at the members-only club that reportedly raised about $10 million for victims of the Oct. 7 Hamas attacks. Mr. Adams was among the attendees.

Wall Street’s favorite local cause

It all amounts to a stark change from the past 20 years, when the city’s homegrown philanthropic engine — Wall Street — championed local charter schools.

For some, the key to addressing struggling public schools, and even entrenched poverty, appeared almost straightforward: create as many charters, which tend to show high standardized test results, as quickly as possible, and then enroll so many children that charters would become a legitimate counterweight to traditional public schools. Charter schools, which are typically not unionized, are overwhelmingly attended by Black and Latino children.

Galas and fund-raisers for charters hosted at one of the luxe Cipriani restaurants or in opulent private homes soon became major events on the city’s social circuit; the schools’ boards filled with finance and business leaders.

High-profile hedge fund managers, including Steven A. Cohen, who now owns the New York Mets, wrote $1 million checks to a pro-charter-school PAC that boosted Republican candidates, part of an effort to counter the influence of the teachers’ union.

But a Democratic political backlash against charters soon swept across the state, and the Legislature eventually curbed the sector’s ability to open new schools, dramatically narrowing the most ambitious goals for charters.

Charter donors were also increasingly frustrated to find protesters — some of whom were affiliated with union-backed groups — demonstrating outside their homes in Manhattan and the Hamptons.

A few billionaires have, however, continued to give lavishly to a small group of charters. The hedge fund manager Kenneth Griffin gave $25 million to Success Academy, the city’s largest charter network, last year. Mr. Bloomberg recently gave Success $100 million and another well-known charter, Harlem Children’s Zone Promise Academy, another $100 million through his charity.

Meanwhile, one of the few recent high-profile philanthropic efforts focused on district schools has fizzled out.

In 2019, the cosmetics billionaire Ronald S. Lauder and the former Citigroup chairman Richard D. Parsons announced a multimillion-dollar campaign that helped block an attempt to eliminate the entrance exam for the city’s elite specialized high schools, which enroll tiny numbers of the Black and Latino students who make up the majority of the school system.

The businessmen funded tutoring for Black and Latino students to prepare for the test. The enrollment statistics did not budge. Mr. Lauder, who has long been one of the city’s most influential donors, quietly disbursed the last of the money in 2021.

He has recently turned his attention outside New York. He has threatened to withhold funding to the University of Pennsylvania, his alma mater, over its response to the Israel-Hamas war.