HAMTRAMCK, Mich. — Leaders of this city met for more than seven hours on a Saturday not long ago, searching for something to cut from a budget that had already been cut, over and over.

This time they slashed money for boarding up abandoned houses, said William Cooper, the city manager. They shrank funds for trimming trees and cutting grass on hundreds of lots left to the city. And Cooper is hoping that predictions of a ferocious snow season prove false; once state road funds run out, the city has set nothing aside to plow streets.

“We can make it until March 1 — maybe,” Cooper said of Hamtramck’s ability to pay its bills. Beyond that? The political leaders of this old working-class city bordering Detroit are pleading with the state to let them declare bankruptcy — a desperate move the state is not even willing to admit as an option under the current circumstances.

“The state is concerned that if they say yes to one, if that door is opened, they’ll have 30 more cities right behind us,” Cooper said, as flurries fell outside his City Hall window. “But anything else is just a stopgap. We’re going to continue to pursue bankruptcy until the door is shut, locked, barricaded, bolted.”

Bankruptcy, increasingly common among corporations and individuals, remains rare for municipalities. Local leaders who want to win elections find it unappealing and often have other choices for solving financial woes.

Besides, states have a say in whether a municipality may pursue bankruptcy at all, and they have every reason to avoid such an outcome, not least of all for fear of a creating a ripple effect that could cripple the municipal bond market and drive up the cost of borrowing.

Yet with anemic property tax revenues and forecasts of more dire financial times ahead, some experts and elected leaders fear more localities may have to at least consider bankruptcy.

“There could be many cities in this position next year,” said Summer Hallwood Minnick, director of state affairs for the Michigan Municipal League, who added that in this state, cities have already struggled with billions less than expected in state revenue sharing. “All our communities have done is cut, cut, cut. They’re down to four-day workweeks and the elimination of parks, senior centers, all of that. So if there’s anything else that happens, they will be over the edge.”

Hamtramck (pronounced ham-TRAM-eck) did not anticipate its current circumstances. Officials in Detroit, Hamtramck’s far larger next-door neighbor, announced this year that they had for years overpaid Hamtramck in a revenue-sharing deal related to a General Motors Co. plant that sits smack on the border of the two cities. The dispute is likely to be resolved, eventually, in court, but meanwhile, Detroit has stopped paying $2 million a year, and Hamtramck is watching a growing gap in its $18 million budget.

Here, the urgent search for services to cut has turned all attention to a realm that is also emerging at the center of budget debates in cities and states around the country: the costs of salaries, benefits and pensions of public workers.

Cooper, the city manager, says that everything else that could be cut already has been, while the city goes on spending 60 percent of its total general fund to pay for its police and firefighting forces — 75 current police officers and firefighters and about 240 former workers and spouses now on pensions. Cooper said that an entry-level police officer costs the city about $75,000 a year in salary and benefits, and yet repeated efforts to renegotiate contracts have failed. “They kind of have the Cadillac plan,” Cooper said, “and we’d kind of like the Chevy.”

The police and firefighters question whether the city’s bankruptcy talk is really just a scare tactic for negotiation. Earlier discussions with city officials, they say, have urged them to accept pay cuts, layoffs, increased worker payments to pensions and even a suggestion that officers might pay for a portion of their own bulletproof vests — all this while the city has opted not to increase taxes.

“Nobody likes the police until you need them,” said Jon Bondra, the incoming president of Hamtramck’s police union.

Although Cooper says he believes bankruptcy, which could allow the city to “start over” with its labor contracts, is the only solution, the authorities in the state of Michigan have so far rejected the city’s request that the governor issue an executive order allowing Hamtramck to file for bankruptcy. An official from the state’s Treasury Department said that no city in Michigan has gone through bankruptcy, and that the governor has no such authority; the state has specific provisions for authorizing a bankruptcy filing, including intervention from an emergency financial manager and an emergency loan board. The current administration, which will be departing later this week, has urged Hamtramck to seek state assistance, including a possible emergency loan.

Rick Snyder, a Republican who is to be sworn in as governor of Michigan on Saturday, said the circumstances in Hamtramck concerned him, particularly for what it might bode elsewhere. “We could have a large number of jurisdictions facing insolvency,” he said. “Major reinvention” will be a necessity, he added, including taking a serious look at the structure of local governments and the possibility, in some places, of consolidation of services.

A new fear is bubbling up along the streets here: that Hamtramck, in so much fiscal angst, may ultimately disappear (either through bankruptcy or, simply, default), and wind up sharing services with or becoming a part of Detroit, a place many here describe as painfully rundown and unsafe.

“I’m not going to wait for two hours for a cop to show up,” said Shannon Lowell, the co-owner of a coffee shop. “We’ve trimmed every bit of fat. What else are we going to do? Borrow money from our dying grandmother?”