Baker administration officials received a skeptical reception in the Legislature on Tuesday as they made their case for a broad set of proposals that they argued are critical for containing the state’s health care costs.

A key part of Governor Charlie Baker’s plan would change eligibility rules and move thousands of people off MassHealth, the state Medicaid program that covers low-income individuals and families. Those people instead would be covered through commercial health insurance.

House and Senate lawmakers rejected these and other elements of the Baker plan in the state budget, saying they didn’t have enough time to vet such significant proposals. But last week Baker asked them to schedule a public hearing and reconsider.

Administration officials have cast their plan as a common-sense approach for ensuring that low-income families have access to health care while tackling the rising costs of MassHealth, a joint state-federal program that covers 1.9 million people in Massachusetts.

The Baker administration, the House, and the Senate have all agreed to one element of the plan: imposing fees on employers to raise $200 million in the next fiscal to help cover state health care costs. But business groups say it’s unfair for them to pay those fees unless the Legislature also accepts the administration’s proposals for cutting costs.

“The cost of inaction is too high,’’ Eileen McAnneny, president of the business-backed Massachusetts Taxpayers Foundation, said at Tuesday’s hearing at the State House.

The administration wants to shift 140,000 adults, including 100,000 parents, from MassHealth onto subsidized commercial health plans. This group of people, earning between $16,240 and $21,600 a year for a household of two, would not have to pay premiums, but they would have higher out-of-pocket costs. They also would have to pay extra for dental benefits or seek dental care at a community health center, where they could get reimbursed for care.

In addition, Baker wants to reestablish a rule that would bar many low-income people from obtaining MassHealth if they have access to affordable health insurance at work.

Baker asked the Legislature to act on his proposals by mid-September. After lawmakers act, Baker can approve or veto their plan.

Karen E. Spilka, the Senate budget chief, called the administration’s proposals “the most sweeping changes’’ to MassHealth since the 1990s. She signaled that lawmakers are reluctant to agree to restrictions to the program’s eligibility.

“There are other ways to get savings than moving people off MassHealth,’’ Spilka, an Ashland Democrat, said at the hearing.

Senator Jason M. Lewis, a Winchester Democrat, said the administration’s plan doesn’t seem to target the underlying costs of health care. “It’s more about moving people between health plans and changing the nature of their insurance,’’ he said.

Other Democratic lawmakers said the administration should propose other steps, such as tackling the high prices charged by doctors and hospitals, before shifting more health care costs onto poor families.

The hearing, which lasted several hours and often delved into the weeds of health policy, included testimony from health care advocates, business groups — and three men with physical disabilities who feared they and others would lose access to certain services through an administration proposal to curb “optional’’ benefits.

Jay Gonzalez, a Democratic former state budget chief who is running for governor against Baker, also testified against the administration’s ideas, which he said went against Massachusetts’ “values.’’

Members of the House and Senate budget and health care financing committees also questioned whether this is the right time to make changes to the state Medicaid program, given the uncertainty around the future of the federal Affordable Care Act.

The Republican-led US Senate on Tuesday agreed to debate repealing and replacing the health care law. Massachusetts Democrats and the state’s Republican governor have raised alarms about the repeal effort, which could result in major cuts to federal spending on health care.

State Representative Jeffrey Sánchez, the newly installed House budget chief, said massive changes to the nation’s health care system “could be one tweet away,’’ apparently referring to President Trump’s penchant for Twitter.

But administration officials said if the Legislature doesn’t act quickly, MassHealth spending will rise by more than $300 million.

“If the federal landscape changes, we’ll be prepared to adjust accordingly,’’ said Marylou Sudders, the state secretary of health and human services.

Sudders said the administration’s plan represents a “balanced’’ approach and “reaffirms our Commonwealth’s commitment to universal health care coverage.’’

Although the legislature has yet to agree to their ideas for changing MassHealth, administration officials have already begun the process of applying for approval from federal officials.

Their plan includes other measures that affect the broader health care market, including establishing a moratorium on new health insurance mandates and allowing for a new type of provider called a dental therapist to provide basic dental care to adults and children.

Priyanka Dayal McCluskey can be reached at priyanka.mccluskey@globe.com. Follow her on Twitter @priyanka_dayal.