WASHINGTON — The Senate Finance Committee voted Thursday to soften the impact of financial penalties that would be imposed on people who did not obtain insurance under sweeping health care legislation.

Members of the committee changed the bill to exempt an estimated two million people who would face financial burdens in buying even the cheapest insurance available. Lawmakers delayed and reduced the penalties for others.

The action, taken by a vote of 22 to 1, came after lawmakers heard an impassioned plea from Senator Olympia J. Snowe, Republican of Maine, who denounced the idea of punishing people who could not afford the insurance they would be required to buy under the legislation. It was the latest indication of the influence that Ms. Snowe has over Democrats as the only member of her party in Congress who has shown any inclination to support President Obama’s drive to overhaul the health care system.

“The obligation should be first and foremost on the United States government to ensure that these plans will be affordable in the marketplace,” Ms. Snowe said. “It surprises me that we would have these high-level penalties on the average American when we have no certainty about whether or not these plans will be affordable. I just don’t understand why there’s this impetus to punish people.”

Under the bill, written by the committee chairman, Senator Max Baucus, Democrat of Montana, “the consequence for not maintaining insurance would be an excise tax,” up to $1,900 a year for a family.

Ms. Snowe and Senator Charles E. Schumer, Democrat of New York, offered an amendment to reduce the penalty and to introduce it gradually. Under their proposal, the maximum penalty for a family would start at $200 in 2014 and rise to $800 in 2017.

The Finance Committee adopted their amendment, which would also eliminate the possibility of criminal penalties for people who went without insurance.

At the same time, the committee decided to exempt a greater number of people from the requirement to have coverage, known as an individual mandate. Under Mr. Baucus’s bill, people would be exempt if they had to pay more than 10 percent of their adjusted gross income for the cheapest available insurance plan. The amendment lowers the threshold to 8 percent of income.

“We should not require anyone to buy a policy they can’t afford,” Mr. Schumer said.

He said two million people would qualify for the exemption, so “two million fewer people will have coverage.” But he said he hoped his proposal would encourage insurance companies to devise lower-cost, more affordable policies.

After seven days of work on the legislation, Mr. Baucus said the end was in sight. A final vote by the committee could come next week, and Democratic leaders said they hoped that the full Senate would begin debate later in the month.

The Finance Committee voted Thursday to impose a variety of new taxes and fees on businesses and some families as a way to help pay for the legislation.

Democrats on the committee turned back Republican efforts to reduce or eliminate the levies, which include taxes on high-cost insurance policies and annual fees on insurers, drug manufacturers and medical technology companies.

Mr. Baucus said the fees and taxes were an essential element of his bill to expand coverage. They embody the concept of “shared responsibility,” he said, and he asserted that the bill, taken as a whole, would reduce taxes for more than 40 million people.

But Republicans said many of the new taxes and fees would hit the middle class, directly or indirectly. Republicans like Senator Michael D. Crapo of Idaho said they were trying to help Mr. Obama keep a campaign promise.

Describing his health care platform in New Hampshire in September 2008, Mr. Obama said: “Under my plan, no family making less than $250,000 a year will see any form of tax increase. Not your income tax, not your payroll tax, not your capital gains taxes, not any of your taxes.”

Republicans tried to amend the legislation to comply with that pledge, but the proposal was rejected, 12 to 11.

“This is a killer amendment,” Mr. Baucus said. “It would gut the president’s program of health care reform.”

Senator Blanche Lincoln of Arkansas, who faces a competitive race for re-election next year, was the only Democrat to vote for the amendment, which stipulated that no new tax, fee or penalty could be imposed on families making less than $250,000.

The bill provides $463 billion in subsidies over 10 years to help lower-income people buy insurance. Senator John Cornyn, Republican of Texas, assailed the subsidies, fees and taxes as “a huge income redistribution.”

House Democratic leaders initially opposed a tax on high-premium health plans, but they have discussed it in the last few days.

More than 60 House Democrats, led by Representative Joe Courtney of Connecticut, told Speaker Nancy Pelosi on Thursday that they opposed the tax because it would fall on many middle-income families.

Mr. Baucus’s bill would set up a commission to recommend ways of curbing the growth of Medicare. Senate Democrats scrambled Thursday to rejigger their health care bill following the discovery that hospitals would be exempted from cuts that might be proposed by the commission.

Hospitals said they were entitled to the exemption because — under a deal reached in July with Mr. Baucus and the White House — they agreed to contribute $155 billion over 10 years to the cost of covering the uninsured.

One purpose of the commission was to depoliticize decisions on Medicare payment policy. But Senator Pat Roberts, Republican of Kansas, said: “The Medicare commission has already succumbed to the hospital lobby. This shows that political deals can still be made.”