An aggressive housing plan promoted by Gov. Kathy Hochul of New York, which she hoped would create 800,000 new homes across the state over the next decade, has fallen apart in Albany after meeting fierce resistance from state legislators.

The plan would have forced cities, towns and villages to allow more housing to be built, and mirrored what other states are already doing. It would have been a first for New York, where home prices and rents have soared to among the highest in the United States and where more than half of all residents spend at least 30 percent of their income on housing.

Ms. Hochul, a Democrat, had sought to shoehorn her housing plan into the state’s budget, which she is still discussing behind closed doors with fellow Democrats who control the State Legislature.

But as negotiations dragged on past the April 1 deadline, the discussions remained deadlocked over Ms. Hochul’s proposed construction mandates for localities. The mandates were heavily opposed by many lawmakers, both Democrats and Republicans, particularly in the State Assembly.

As the sides appeared unable to reach agreements on other thorny housing policies, including tenant protections, the negotiations began to unravel. After hitting an impasse this week, the governor’s housing plan, as well as other major housing policies, were pulled from the state budget discussions, according to three officials familiar with the private deliberations.

Officials from the New York City suburbs in Westchester County and on Long Island had resisted the effort fiercely, saying it was heavy-handed and would have strained local services.

Why did the governor focus on New York City’s suburbs?

The plan did not single out suburbs. It called for each community in the state to make way for more residential development. But some of the most significant effects would have been felt in towns and villages on Long Island and in Westchester County that have mass transit stations but have allowed relatively few homes to be built over the decades.

By one measure, Westchester County and Suffolk and Nassau Counties on Long Island have allowed fewer homes to be built per person in the past decade than the regions around nearly every other major U.S. city, including Boston, San Francisco and Washington.

The lack of building has contributed to a statewide housing shortage. A December report from the nonprofit Regional Plan Association estimated that New York needs to add more than 817,000 homes in the next decade to keep up with population growth and ease overcrowding.

The New Jersey suburbs offer a contrast and illustrate the potential economic benefit of building.

From 2000 to 2017, the number of people who commuted to New York City from the surrounding areas grew by around 190,000, according the Department of City Planning. About two-thirds of those people lived in northern New Jersey, where more housing was built than on Long Island and in the Hudson Valley combined.

In addition to easing the shortage, Ms. Hochul’s plan was meant to address a history of segregation in suburban communities, which in many cases were designed to exclude Black people.

What would her proposal have done?

The plan included two major components.

One would have forced every city, town and village that regulates land use to expand its housing stock every three years by set percentages — 3 percent downstate and 1 percent upstate.

Another would have compelled communities to allow more housing density near rail stations, including an average of at least 50 homes per acre within a half-mile of many Long Island Rail Road and Metro-North stations that were within 15 miles of New York City’s borders.

If a city or town had rejected a development improperly or did not meet its percentage targets, a fast-track process that would have overridden local opposition would have been triggered. The provision, state officials say, was important because it essentially ensured that growth would occur.

The plan would have had a modest effect in some places: Almost 80 percent of municipalities outside New York City would need to add fewer than 50 homes in the first three years to meet the growth targets.

Others, particularly communities near New York City that are dominated by single-family homes — Bronxville in Westchester, for instance, or Oyster Bay Cove in Nassau County — might have experienced significant changes.

What did suburban officials have to say?

Suburban officials from across the political spectrum led a fierce resistance to the proposal.

Andrea Stewart-Cousins, the Democratic leader of the State Senate, rebuffed the plan. Ms. Stewart-Cousins, who represents part of Westchester County, has said the state should create incentives for building homes instead of requiring it, even though research and history show that such strategies rarely succeed.

In Westchester, more than two dozen mayors and town supervisors signed a letter last month criticizing Ms. Hochul’s plan. Republicans, particularly on Long Island, united behind calls for “local control, not Hochul control.”

A few Democratic officials — like Steve Bellone, the Suffolk County executive, and Phil Ramos, a Long Island assemblyman — supported Ms. Hochul’s plan.

“It doesn’t matter what kind of incentive you give them — a wealthy community, before they allow Black and brown people in, they’ll walk away from any amount of money,” Mr. Ramos said at a recent rally.

What will happen next?

While it appears the plan will not make into the state budget, which lawmakers often use to pass contentious measures, officials could revisit it later in the legislative session, which ends in June.

When asked about the plan’s collapse, a spokeswoman for Ms. Hochul referred to an earlier statement where she took a jab at lawmakers for opposing “core elements” of the housing plan, saying that “merely providing incentives will not make the meaningful change that New Yorkers deserve.”

Also left on the cutting room floor were other housing measures, from tenant protections to the extension of a contentious tax-break program for real estate developers known as 421a.

One of the proposals would limit a landlord’s ability to raise rents. The proposal, favored by progressive Democrats and tenant activists, has been a flashpoint in Albany for years, and is opposed by Ms. Hochul, a moderate Democrat.

Lawmakers could take up housing policy, which Democrats say is a party priority, after they approve a final budget.