WASHINGTON — Fearing a backlash, Democrats smoothed the impact of sweeping health care legislation on working-class families Thursday night and steered President Barack Obama’s top domestic priority toward a crucial Senate advance. The most far-reaching overhaul in decades aims to protect millions who have unreliable coverage or none at all.

Republicans on the Senate Finance Committee attacked the bill as riddled with tax increases that violated Obama’s campaign promises, but failed to remove any of them.

After marathon public debate, agreement by the committee is all but certain for the legislation, although no final vote was expected until next week. That formality — Democrats hold a 13-10 majority on the panel — will clear the way for the full Senate to begin work on the measure at mid-month.

The legislation, like a companion bill under construction in the House, would bar insurance companies from denying coverage or charging higher premiums on the basis of pre-existing medical conditions. It also includes federal subsidies to make insurance available to millions who lack it, and it takes steps to slow the skyrocketing growth in health care costs nationwide.

Supporters said the overhaul’s cost was in the range that Obama has set, about $900 billion over a decade, and would not raise federal deficits. Gradually, health care has grown to dwarf all other issues in Congress, and is causing supporters and opponents to spend more than $1 million a day on television advertising to sway the outcome.

After days spent largely turning aside Republican calls for changes in the bill, Senate Democrats coalesced behind two of their own that could alter the legislation in significant ways.

One, backed by Sen. Maria Cantwell, D-Wash., would allow states to negotiate with insurers to arrange coverage for people with incomes slightly higher than the cutoff for Medicaid, the government health care program for the poor.

The second, which passed on a 22-1 vote, would exempt millions of people from a requirement to purchase insurance that is currently in the bill and reduce the penalties on millions more who defy the mandate.

“First and foremost we have an obligation to show we achieved the goal of affordability, which is what this legislation is all about,” said Sen. Olympia Snowe, R-Maine, who worked with Democrats on the change and is the only Republican in Congress viewed as a potential supporter of the overall legislation.

Originally, the bill required individuals and families to buy coverage as long as it cost no more than 10 percent of their income. Under the change, that would be lowered to 8 percent.

Sen. Chuck Schumer, D-N.Y., acknowledged the result would be an estimated 2 million additional individuals and families staying uninsured in comparison with the original bill.

But he noted that the amendment overall was designed to shield “people solidly in the middle class” from an undue burden.

Republicans and even some Democrats had cautioned against a voter backlash if the bill imposed too great a burden on working families, particularly with the country recovering from the worst economic crisis in decades.

The bill had said that those ignoring the purchase requirement would have to pay a maximum penalty of $750 for individuals and $1,900 for families.

Under the change, no penalty would apply until 2014, when the maximum would be $200 for individuals, rising to $750 in 2017. The maximum for families would reach $1,500 the same year.

The Cantwell proposal is based on a system in Washington state that she said results in lower-cost, high-quality coverage, generally delivered through managed care, as the state uses its purchasing power in negotiations with insurers.

Republicans questioned whether the impact would be to raise insurance premiums for others, and said they were fearful the result would be to reduce health care options.

Cantwell said the first concern was unfounded, and added Washington currently has as many as four choices for residents currently covered by the state program. As for the second Republican point, she responded, “If your governor and your legislators don’t want to negotiate on behalf of their citizens, that’s their political problem.”

The provision passed, 12-11, on a near party-line vote.

It is designed to allow coverage for individuals and families between 133 percent of poverty and 200 percent of poverty. For individuals, that means incomes between $14,403 annually and $21,660. For families of four, the eligibility would be $29,326 to $44,100. Aides said 30 million or more of the nation’s uninsured are in that income range.

Approval by the Finance Committee would clear the way for Senate Majority Leader Harry Reid to merge the bill with one approved earlier by the Senate Health, Education, Labor and Pensions Committee. One bill permits the government to sell insurance in competition with private companies, a provision referred to as a public option. The measure in the Finance Committee does not.

“I favor a public option. We’re going to do our very best to have a public option,” Reid said.

The day opened with Republican attacks on tax increases in the legislation, including one that makes it more difficult for taxpayers to itemize deductions for health care. Sen. Mike Crapo, R-Idaho, quoted Obama repeatedly as pledging last year that his health care plan would not raise taxes on any individual making more than $200,000 or family with incomes over $250,000.

Baucus said the GOP attempt to rescind the tax increases, if adopted, would cripple the drive to overhaul health care. He said that, overall, the legislation provides for a net cut in taxes rather than an increase, and Democrats blocked the GOP maneuver.

Across the Capitol, Democratic leaders in the House met privately with moderate members of the rank-and-file, with liberals, and then with first-termers as they struggled to achieve a consensus on legislation to bring to the floor. Majority Leader Steny Hoyer announced at midday it would probably be at least two more weeks before House legislation was ready.

Under the bills in both houses, most insurance policies would be required to cover preventive care as well as treatment for illnesses, surgery, vision, dental and mental health care.

In general, the legislation is designed to encourage employers to retain coverage they now provide, and workers to remain enrolled. Policies would be available — for those who have coverage and those who don’t — through so-called insurance exchanges.

For the first time, individuals would be under the requirement to purchase insurance or face penalties. To help the lower-income buy insurance and prod small businesses to offer it, federal subsidies would be available on a sliding scale to defray the cost of premiums.

The costs would be borne through a variety of taxes on health care providers, as well as hundreds of billions of dollars in cuts in projected Medicare and Medicaid spending.