More than two years after the first buses of migrants began arriving from the southern border, New York is running short on time, money and public sympathy to support the hundreds of thousands of migrants who have settled here.

The city is facing a budget crunch and a once-in-a-generation affordability problem and cannot indefinitely provide asylum seekers with shelter, housing and other services. At the same time, migrants desperate to work have struggled to find jobs.

Enter one of New York’s pillars of power: big money.

After largely staying on the sidelines of the migrant crisis, a group of influential philanthropies is planning to spend millions of dollars this fall on efforts to make asylum seekers more self-sufficient and eventually able to contribute to their new home.

On Thursday, the Carnegie Corporation of New York plans to announce a $4 million donation to the city’s public libraries, in part to expand English language classes popular with migrants.

“The faster immigrants are integrated and can speak English, the sooner they will be able to work” and pay taxes, said Dame Louise Richardson, the group’s president. “It’s a virtuous circle.”

Two other philanthropies — the Robin Hood Foundation and the New York Community Trust — will together spend at least $4 million on a separate effort to bolster nonprofits that have been on the front lines of the crisis, connecting migrants stepping off buses at Port Authority with shelter, food, schools, legal assistance and job training.