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.