For four days, Mayor Zohran Mamdani and City Council leaders had been locked in a heated disagreement over an expensive rental assistance program.

Julie Menin, the Council speaker and a relative moderate, wanted to expand the program to help not just the homeless, but also certain renters facing eviction. Mr. Mamdani, a democratic socialist, argued for fiscal restraint.

By Monday night, just a day before the roughly $125 billion budget is due, the dispute appeared to be nearing a resolution — seemingly ending what had been a prolonged battle that involved tense phone calls between Mr. Mamdani and Ms. Menin as well as their staffs, with the mayor’s team going around the speaker to meet directly with individual Council members.

The mayor’s opposition may seem to contradict his core ambition to expand the social safety net for working-class Americans. But Mr. Mamdani has also shown himself to be a pragmatist keenly aware that his management of the nation’s largest city is under close scrutiny from bipartisan skeptics who doubt that a 34-year-old democratic socialist can effectively govern the financial capital of the United States.

And so this weekend’s dispute has taken on something of a role reversal, with Mr. Mamdani pushing against the expansion of a social safety net program that Ms. Menin has championed.

At issue is an increasingly expensive housing voucher for homeless New Yorkers known as the City Fighting Homelessness and Eviction Prevention Supplement, or CityFHEPS, which pays a portion of eligible New Yorkers’ rent. Between 2019 and 2026, the program’s cost grew to $1.7 billion from $25 million, according to the Citizens Budget Commission. The City Council has been seeking an additional $300 million a year in city spending. The mayor’s office has proposed just $175 million, with $50 million coming from the City Council’s discretionary funds. By Monday night, the two sides were nearing a deal for Mr. Mamdani’s administration to spend $125 million a year on the voucher program.

By late Monday afternoon, the mayor and Council leaders were nearing a compromise on a new program that would change the eligibility criteria for who would qualify. The existing program had been open to people who earned less than 200 percent of the federal poverty line. The new one would be available to those who earn 50 percent of the area median income, a more generous metric. For a family of three, that would expand benefits to families earning as much as $76,000, up from the current level of about $54,000, according to a person briefed on the negotiations.

The existing 10-hour-a-week work requirement would be eliminated, and the voucher would be offered to rent-regulated tenants facing eviction, rather than all tenants facing eviction, the person said. It would not be an entitlement program, and its budget would be capped.

The deal remains in negotiation and could change.

The bitter tenor of the back-and-forth stands in contrast to a recent string of success for the mayor, who secured a rent freeze for nearly one million rent-regulated apartments last week and enjoyed an election night sweep for his preferred state and congressional candidates. Some of his candidates vanquished opponents who have allies in the Council.

Ms. Menin has been able to harness that anger toward the mayor and her members’ belief in the voucher program to unite disparate factions of the Council behind her.

The mayor’s team tried to counter Ms. Menin’s strategy by using its briefings with individual Council members to offer funding commitments to various projects, according to several people familiar with the private discussions. A spokesman for the mayor countered that it was the Council members who had sought out information from the mayor’s office. Separately, the administration has asked allies to intercede on its behalf, two people said.

As a result, Mr. Mamdani’s first go at budget negotiations — typically a routine dance that plays out over months — were nearly undone by an unusual level of acrimony.

In recent years, “the sides have not ever been quite so dug in,” said Louis Cholden-Brown, the former deputy counsel to the Council speaker.

The voucher program was created in 2018, and the Council voted to expand it in 2023 to encompass not merely New Yorkers living in homeless shelters, but to also include renters facing eviction. Former Mayor Eric Adams vetoed the expansion, arguing that it would unduly strain the budget. After the council overrode the mayor’s veto in 2024, Mr. Adams refused to enforce the laws, prompting the City Council to sue.

During his successful mayoral campaign, Mr. Mamdani promised to drop the litigation if elected and expand the program.

But campaigning is not governing, and after taking office and taking stock of the city’s fiscal constraints, Mr. Mamdani reversed course. He cited the need for fiscal responsibility at an uncertain economic time.

About 67,000 households now use CityFHEPS. Some officials worried that existing tenants facing eviction would outcompete shelter residents for scarce apartments, and that any significant expansion of CityFHEPS would only compound what are already predicted to be significant budget gaps next year and beyond. That concern was echoed by the new city comptroller, Mark Levine, who in January said that the existing program was expanding at an unsustainable rate.

“At a growth rate of 4 percent a month, this means a doubling every year and a half,” he said at the time.

The expansion currently being contested in court could cost as much as $20 billion over five years, Mr. Levine said. Negotiations around the settlement of the litigation and the budget negotiations are happening in parallel, the person familiar with the talks said.

Proponents for expanding the CityFHEPS program say it would save the city money, because helping pay someone’s rent is cheaper than operating a shelter bed, on a per-diem basis. The City Council also argues that any agreement should include guardrails that would contain costs.

“The Council has been ready to agree to a budget that protects vulnerable New Yorkers, ends the costly litigation and creates a responsible, sustainable framework for managing CityFHEPS over the long term,” Ms. Menin said in a statement. “These are all essential priorities, and we remain committed to achieving them together.”

The issue of CityFHEPS explosive growth has alarmed budget watchdogs, in part because the shelter population has continued to increase in tandem with the growth in spending on CityFHEPS, according to the Citizens Budget Commission.

While the city can use state and federal funding to run shelters, the vouchers are entirely paid by the city, the commission and City Hall said.

And shelter stays might be temporary and sporadic, while annual rental payments are a much bigger commitment, both the group and city officials said. Finally, rents continue to rise in the city, meaning that even if the population of voucher holders were to remain stagnant, the cost of those vouchers would still increase.

“Mayor Mamdani is committed to protecting CityFHEPS, and this administration has already invested billions of dollars in the program to address years of chronic underbudgeting left by the previous administration,” Joe Calvello, a spokesman for the mayor, said in a statement. “But we cannot ignore the fiscal realities facing our city; it is government’s responsibility to be careful stewards of taxpayer dollars.”

Proponents for the voucher expansion argued the government has other responsibilities, too.

“Every day that delays, it’s more children growing up in shelter,” said Christine Quinn, the former Council speaker who now runs a major homeless services organization. “This settlement should have occurred on Day 1 in his administration. The mayor has flip-flopped on his promise and this needs to be resolved in the budget immediately.”