Now the focus of heavy lobbying, state senators have largely remained silent about collective bargaining and municipal health care since the House passed a plan this week to curb the negotiating power of local unions over their health care benefits.

Senators appeared hesitant and even uneasy Thursday about laying out their views on the issue. Most contacted by the News Service said they were unaware of the specifics of the House proposal, which thrilled business and municipal management groups and enraged labor officials after it was adopted late Tuesday night.

Amid the uncertainty, two points of agreement between proponents and opponents of the House proposal appear to have taken shape: Labor unions should continue to have “a voice” in determining their health care costs, and the Legislature should help cities and towns find a way to save tens of millions of dollars on their health care bills. It’s the critical details that are still fuzzy.

Senate President Therese Murray set the tone Wednesday by acknowledging she had yet to read the House’s proposal but was pleased that the House had “moved the needle” on the thorny issue.

The Senate is preparing to unveil its fiscal 2012 budget proposal in mid-May, and members say they haven’t decided whether municipal health and collective bargaining would be included in the proposal.

Sen. Katherine Clark, a Melrose Democrat and the co-chair of the Committee on Public Service, said senators were reviewing the House proposal.

“I have a serious concern about making sure we giving retirees a voice,” she said, adding that she supports a provision to move all eligible retirees to Medicare.

Clark also said she supported the House’s proposal that would allow cities and towns to choose whether to cut collective bargaining in favor of unilateral control over premiums and deductibles. Gov. Deval Patrick on Wednesday questioned the local option, arguing that reform should be mandatory to ensure savings for cities and towns.

“I think the local option is an important part of the House bill,” Clark said. “We need to give municipalities the tools to make decision that will be in their own best interest.”

Asked whether the local option could serve as a deterrent to allowing city and town managers to take advantage of reforms, Clark said she was unconcerned.

“I believe municipalities are feeling the impact of this budget through their services. I think communities will have more than enough incentive to seek savings,” she said.

Sen. Thomas McGee said he was unaware of the specifics of the House proposal but said he hoped that whatever the outcome of the debate, municipal workers should have “a voice in the process” of setting their health care co-pays and deductibles. He noted that in each of the last two years, the Senate has adopted plans that would have authorized cities and towns to set co-pays and deductibles for their workers while sharing the savings with the affected employees.

The House’s plan, adopted Tuesday night on a 111-42 vote, would permit cities and towns who opt to forgo collective bargaining to unilaterally set co-pays and deductibles for their workers. After unveiling a plan, municipal officials would convene a committee of public employee unions to confer on the details of the proposal and recommend changes. If city and town managers fail to agree on a plan with unions, they would be forced to share 20 percent of any avoided costs with their workers. A successful agreement would require that cities and towns share just 10 percent of their savings.

Supporters of the plan say it would ensure that state and municipal investments in public safety and education won’t be swallowed up by ever-increasing health care costs and that it could save cities and towns $100 million in the first year of implementation.

Labor officials flooded the State House on Tuesday and Wednesday, excoriating House Democrats for voting to take away bargaining power and comparing their proposal to far more sweeping crackdowns on unions in Wisconsin and other Republican-controlled states. Teachers turned out to lobby Thursday just as the House budget that includes the muni-health reform proposal was approved 157-1.

Despite the outrage from union officials, Rep. Martin Walsh (D-Dorchester), who led the drive against the House’s proposal and countered with a union-supported push of his own, described a natural alliance between Democrats and labor and said he believed the rift would be temporary.

“We’re going to have differences. This is a very big difference. But the Democratic Party and the labor movement have always worked together,” he told the News Service. “We’ve always worked our differences out and there’s still a ways to go before we have a final version … and I’m sure by the end we’ll work things out.”

“There’s always another issue. There’s always going to be another election,” he continued. “You win some, you lose some. I’ve lost a lot of battles in this chamber. I’ve won a lot of battles. I’ve learned, it’s very difficult to hold a grudge. It kind of stunts growth and progress.”

Tuesday’s House vote preempted deliberations by the Legislature’s Committee on Public Service, which took several hours of public testimony on plan design and collective bargaining over municipal health care but has yet to issue recommendations for legislation.