As Montgomery County enters the critical week in its charged budget fight, politicians and public employee unions are feeling their way through unfamiliar and potentially treacherous territory, the result of the County Council’s unusually aggressive role in collective bargaining.

The all-Democratic council has pushed its way into the process that sets salaries and benefits for thousands of government workers, seizing a hands-on role in negotiations from which it had long sought to keep a distance.

In a series of closed-door meetings in recent days, the council has given the county’s union leaders and representatives of County Executive Isiah Leggett’s administration its own plan for cutting employee health and retirement benefits.

Instead of the $29.6 million in benefits cuts Leggett proposed for county government employees, police and firefighters — which prompted a union outcry — the council proposed about $14 million in cuts for the next fiscal year.

The council proposes making up the difference, and possibly more, by cutting funds covering benefits for teachers and other public school workers.

Although some union leaders had said they welcomed the chance to deal directly with the council, early reaction has been chilly. Police union officials are particularly frustrated by the actions of Leggett, and now the council.

“This has created turmoil within the police department, and it’s affecting officers on the street. We need to get everything resolved,” said Walt Bader, a top police union official. “All this uncertainty is creating great concern, and their minds are not 100 percent on their job. . . . It’s in everybody’s interest to have some labor peace out here.”

Teachers, who would feel some of the cuts police and other government workers would avoid, are also displeased. Some were planning lunchtime “grade-ins” at a handful of malls Saturday, grading student work at food courts to underscore how their jobs come home with them at night and on weekends.

“You can’t do something that affects the take-home pay of folks who are in front of kids every day and say that doesn’t have an effect on the classroom, because it does,” said Montgomery teachers union President Doug Prouty. “You can’t expect it not to have an effect on their sense of themselves and their sense of themselves related to work.”

Under local law, the county executive is supposed to do the bargaining with government employees over such things as medical benefits, and when talks get stuck, labor arbitrators are called in to choose who they think is being more reasonable. But it’s the council that has the legal authority to decide what money gets spent on such benefits — and everything else.

That disconnect has led to some dysfunction, with bargaining results at times having little or no grounding in the fiscal realities being weighed by the council, or the political preferences of the body’s nine members.

Some council members acknowledged that they’ve made no one happy. But they say given the need to find real, multiyear cuts to deal with a sharp drop-off in revenue, it’s vital to be clear about where they are headed.

“This is a way of saying, ‘You all need to know what we’re thinking.’ Since we’re the ones that are going to pull the trigger on the budget, we should talk,” said council member Marc Elrich (D-At Large). “In these times, and given where we are, everybody ought to play straight with everybody. That would be a change.”

Said council President Valerie Ervin (D-Silver Spring): “This is not a status-quo moment. Things are going to change.”

The council’s budget proposals were made this week during bargaining talks that were set up to be confidential.

Among the proposals is one to raise employee pension costs, which largely affects the police, fire and other public safety workers covered by those more generous retirement plans. The increase would be about half of what Leggett called for in the first year but reach the level Leggett had proposed in the second year and beyond.

The council also proposed finding additional long-term savings by capping cost-of-living increases for pensions. It would affect existing and future employees in different ways. To address the county’s vast retiree health-care liability, the proposal also calls for new hires to work 10 years instead of five before becoming eligible for the minimum level of county-subsidized health insurance after retirement.

The council would also shift some of the costs of medical coverage to employees, though not as much as Leggett proposed.

Employees would pay 25 percent of their premiums, as opposed to at least 20 percent, which is how it works currently. That and other health-plan changes would cost someone with a higher-end family plan $1,180 more a year, according to a county analysis. Leggett had called for the employee share to be raised to at least 30 percent starting July 1. The council’s proposed increase would begin Jan. 1.

To encourage employees to join HMOs, which are cheaper for the county, the council proposal would keep the 20 percent employee share for those who stayed in such plans or who moved into them.

Bargaining talks continue next week, with key budget votes by the full council scheduled for Thursday.