BOSTON -- Gov. Charlie Baker’s plan to charge a fee to companies that don’t offer health insurance to a majority of their employees is winning support from skeptical Statehouse Democrats, but only with more public input amid a backlash from the business community. 

House Democratic leaders unveiled their version of the fiscal 2018 budget on Monday. The $40.3 billion spending package increases aid for local governments and schools, boosts funds for early education and substance abuse programs, and doesn’t raise taxes or tap the state’s reserve fund.

While the House budget doesn't outright reject Baker’s fee proposal, it doesn’t completely embrace it, either.

Instead, the plan directs the state to hold public hearings and solicit input from the business community before deciding who should be charged for shuffling employees onto government-subsidized health insurance.

House leaders are also questioning the Baker administration’s revenue estimates. Their budget scales down money expected from the health insurance fee from $300 million to $180 million in the coming budget year, citing new figures that show declining private sector enrollment in MassHealth, the state’s Medicaid program.

“Basically what we’re saying is, ‘You can go forward with this, but let’s find a better way to do it,’” said Rep. Brian Dempsey, House Ways & Means Committee chairman, at a briefing Monday. “There ought to be a process for the business community to weigh in on it.”

The key provision of Baker’s 2018 budget, filed in January, calls for a $2,000 per person fee on businesses with 11 or more workers that don’t provide insurance to at least 80 percent of their employees.

To be exempt from the fee, employers would need to cover 60 percent of premium costs for workers participating in company plans.

Baker, a Republican, argues that the fees are needed to offset costs of hundreds of thousands of private sector workers and their family members being absorbed by government-backed insurance plans such as MassHealth and the Health Connector. About 380,000 people have switched from employer to government plans in recent years.

Business groups say the fee unfairly penalizes employers for health care decisions made by workers.

"It would force employers to fix a problem they didn't create," said Chris Geehern, a spokesman for Associated Industries of Massachusetts, a powerful lobbying group. "The reality is most companies are doing the right thing and shouldn't be punished."

Geehern said AIM continues to oppose the assessment but supports the House plan to open up Baker's proposal to more public scrutiny.

"This would give everyone some breathing room, and create a more open and transparent debate to what is a really complex issue," he said.

Baker’s proposal resurrects a so-called “fair-share contribution” that was once part of the state’s health care system, which was signed into law in 2006.

The initial mandate, which assessed $295 per employee, was repealed in 2013 as lawmakers and former Gov. Deval Patrick sought to comply with the federal health care reform law.

Dempsey, a Haverhill Democrat, said House leaders support Baker’s plans to seek a waiver from federal rules to force full-time workers to take employer coverage, when available, and not choose government-subsidized plans.

Under the Affordable Care Act, the state cannot prevent private sector employees from choosing Medicaid, even if they are are also offered employer coverage.

“The crux of the issue is that we have seen a 7 percent enrollment shift from commercial plans to MassHealth under the ACA,” Dempsey said. “This isn’t exclusive to Massachusetts. This is happening across the country.”

Costs for MassHealth are projected to increase 4 percent -- by more than $322 million -- in the budget year that begins in July. MassHealth covers more than 1.9 million people, according to state data.

Baker has pledged to rein in the cost of MassHealth, which consumes about 40 percent of the budget. But House Democrats have also rejected his money-saving plans to cap state payments to some insurance providers and impose a moratorium on new insurance mandates.

Noah Berger, president of the Massachusetts Budget and Policy Center, said charging employers an assessment for not fully covering their workers "would provide the state with revenue to offset the cost of providing insurance when employers don't."

"That makes it possible to balance the budget without relying on painful program cuts," he said.

Overall, the House budget would increase state spending by 3.8 percent next fiscal year -- $180 million less than Baker's initial $40.5 billion spending package.

Aid to cities and towns, used for everything from closing local budget gaps to fixing sidewalks, would increase by $40 million to $1.06 billion.

Education aid would increase $106 million over the current year to $4.7 billion under the plan.

The House budget also includes spending increases for early education, substance abuse programs, mental health, regional school transportation and raises for day care and preschool teachers.

“This budget is fiscally responsible while making targeted investments that ensure we care for the most vulnerable amongst us,” House Speaker Robert DeLeo, D-Winthrop, told reporters on Monday. “It’s a very strong package.”

Lawmakers are expected to file hundreds of proposed amendments to the budget by the end of the week, the fate of which will be debated in closed-door leadership negotiations.

The Senate is expected to unveil its budget in May.

Christian M. Wade covers the Massachusetts Statehouse for North of Boston Media Group’s newspapers and websites. Email him at cwade@cnhi.com.