WASHINGTON — Senators of both parties said Thursday that they would seek significant changes in a Democratic proposal to tax generous high-cost health insurance policies.

The tax, proposed as a way to help finance coverage of the uninsured, would be levied on insurance companies. But the senators said they worried that it would be passed on to individual policyholders, families and employers who buy insurance for their workers.

The tax is in a sweeping health care bill unveiled on Wednesday by the chairman of the Senate Finance Committee, Max Baucus, Democrat of Montana. It would raise $215 billion over 10 years, offsetting about one-quarter of the cost of the bill.

Many Democrats said they were also concerned that insurance would still be unaffordable to many middle-income people, even with tax credits and subsidies proposed by Mr. Baucus.

Senator Olympia J. Snowe, Republican of Maine, voiced the same concern. In an interview with The New York Times and CNBC, Ms. Snowe said that for her to support the bill, “there would have to be more subsidies” for low- and middle-income people and that she was trying to figure out how to pay for them.

Ms. Snowe said “the time has come” to pass comprehensive health legislation. But she added that it was important to get the policy and the details right, because they would affect every American.

After listening to his colleagues on Thursday, Mr. Baucus said he was “fully open” to suggestions on modifying his bill.

In a speech Thursday to students at the University of Maryland, President Obama described the fight over health care as a “defining struggle of this generation.” Recalling the struggles for civil rights and women’s voting rights, Mr. Obama said the United States was “the only nation on earth that leaves millions of people without health insurance.”

Democrats and Republicans seemed to retreat into partisan camps on Thursday and huddled to chart strategy. The Finance Committee intends to vote on the Baucus bill next week.

Under Mr. Baucus’s plan, the new tax would apply to health insurance plans with annual premiums exceeding $8,000 for individuals and $21,000 for families. He said it would apply to a small number of health plans.

But other senators said they feared that the insurance tax, like the Alternative Minimum Tax on personal income, would affect more and more people over time. The threshold amounts would rise with the Consumer Price Index, which is increasing more slowly than the costs of health care and health insurance.

Senator John Kerry, Democrat of Massachusetts, who first proposed the insurance tax, said Mr. Baucus had set the thresholds too low. As a result, Mr. Kerry said, “working folks with a lower level of income will get dragged in,” and the tax could affect union members who have sacrificed pay raises to get health benefits.

Mr. Kerry said the threshold for family coverage should be at least $24,000.

Senator Charles E. Grassley of Iowa, the senior Republican on the Finance Committee, expressed concern about the effect of the tax on “middle-class consumers.”

“The whole goal here is to reduce costs to policyholders,” Mr. Grassley said. “This tax will increase costs.”

Senator Kent Conrad, Democrat of North Dakota, defended the proposal. By reducing the current tax subsidy for employer-provided health benefits, he said, the proposed tax would slow the growth of health spending. Under current law, employee health benefits are not counted as taxable income for workers.

In the Senate and the House, liberal Democrats stepped up the push for a government-run insurance plan. They cited a report from the Congressional Budget Office that said the alternative proposed by Mr. Baucus, nonprofit insurance cooperatives, would not provide much competition for private insurers.

Representative Keith Ellison, Democrat of Minnesota, said the co-ops would be “too small and too weak to compete with insurance companies that have been in the game for a long time.”

Senator Dianne Feinstein, Democrat of California, said she was concerned about a provision that could block construction of some hospitals in her state.

Senator Robert Menendez, Democrat of New Jersey, said he feared that the bill’s prohibition on assistance for illegal immigrants would adversely affect children who are United States citizens. Still, Mr. Menendez said he thought a bill would pass.