WASHINGTON — Americans who refuse to buy affordable medical coverage could be hit with fines of more than $1,000 under a health care overhaul bill unveiled Thursday by key Senate Democrats looking to fulfill President Barack Obama’s top domestic priority.

The Congressional Budget Office estimated the fines will raise around $36 billion over 10 years. Senate aides said the penalties would be modeled on the approach taken by Massachusetts, which now imposes a fine of about $1,000 a year on individuals who refuse to get coverage. Under the federal legislation, families would pay higher penalties than individuals.

In a revamped health care system envisioned by lawmakers, people would be required to carry health insurance just like motorists must get auto coverage now. The government would provide subsidies for the poor and many middle-class families, but those who still refuse to sign up would face penalties.

Called “shared responsibility payments,” the fines would be set at least half the cost of basic medical coverage, according to the legislation.

In 2008, employer-provided coverage averaged $12,680 a year for a family plan, and $4,704 for individual coverage, according to the Kaiser Family Foundation’s annual survey. Senate aides, who spoke on condition of anonymity because they were not authorized to speak publicly, said the cost of the federal plan would be lower but declined to provide specifics.

The legislation would exempt certain hardship cases from fines.

The new proposals were released as Congress neared the end of a weeklong July 4 break, with lawmakers expected to quickly take up health care legislation when they return to Washington. With deepening divisions along partisan and ideological lines, the complex legislation faces an uncertain future.

Obama wants a bill this year that would provide coverage to the nearly 50 million Americans who lack it and reduce medical costs.

In a statement, Obama welcomed the legislation, saying it “reflects many of the principles I’ve laid out, such as reforms that will prohibit insurance companies from refusing coverage for people with pre-existing conditions and the concept of insurance exchanges where individuals can find affordable coverage if they lose their jobs, move or get sick.”

The Senate Health Education, Labor and Pensions bill also calls for a government-run insurance option to compete with private plans as well as a $750-per-worker annual fee on larger companies that do not offer coverage to employees.

Sens. Edward M. Kennedy, D-Mass., and Christopher Dodd, D-Conn., said in a letter to colleagues that their revised plan would cost dramatically less than an earlier, incomplete proposal, and help show the way toward coverage for 97 percent of all Americans.

In a conference call with reporters, Dodd said the revised bill had brought “historic reform of health care” closer. He said the bill’s public option will bring coverage and benefit decisions driven “not by what generates the biggest profits, but by what works best for American families.”

The two senators said the Congressional Budget Office put the cost of the proposal at $611.4 billion over 10 years, down from $1 trillion two weeks ago.

However, the total cost of legislation will rise considerably once provisions are added to subsidize health insurance for the poor through Medicaid. Those additions, needed to ensure coverage for nearly all U.S. residents, are being handled by a separate panel, the Senate Finance Committee. Bipartisan talks on the Finance panel aim to hold the overall price tag to $1 trillion.

The Health Committee could complete its portion of the bill as soon as next week, and the presence of a government health insurance option virtually assures a party-line vote.

In the Senate, the Finance Committee version of the bill is unlikely to include a government-run insurance option. Bipartisan negotiations are centered on a proposal for a nonprofit insurance cooperative as a competitor to private companies.

Three committees are collaborating in the House on legislation expected to come to a vote by the end of July. That measure is certain to include a government-run insurance option.

At their heart, all the bills would require insurance companies to sell coverage to any applicant, without charging higher premiums for pre-existing medical conditions. The poor and some middle-class families would qualify for government subsidies to help with the cost of coverage. The government’s costs would be covered by a combination of higher taxes and cuts in projected Medicare and Medicaid spending.