WASHINGTON — In a bid to unify Democrats in support of his health-care-overhaul bill, Senate Finance Committee Chairman Max Baucus, D-Mont., on Tuesday proposed boosting subsidies for financially strapped people who would be required to buy insurance.

He also slashed proposed penalties for noncompliance with the insurance mandate and sought to limit how many people would be subject to a new excise tax on so-called “Cadillac” health plans.

Baucus’ proposals came on the first day his committee began reworking the long-awaited blueprint.

His initial proposal faced a barrage of criticism from Democrats and from the only Republican senator sympathetic to the bill, who said families of moderate means would not be able to afford the new mandate requiring almost everyone to have health insurance.

Baucus’ quick response was a sign of the growing pressure on him to move to the left now that hope of winning significant GOP support has all but evaporated.

Baucus’ changes drew praise Tuesday from some Democrats and from Sen. Olympia Snowe, R-Maine.

“This is a solid starting point, but we are far from the finish line,” said Snowe, whose support is being courted by Baucus and the White House.

Most Republicans continued to lambaste the Democratic effort.

“As this bill moves across the (Senate) floor, I am concerned that it will not move more in the direction of more choice and lower cost, but one that will lurch to the left and result in higher cost and less choice for the American people,” said Sen. John Cornyn, R-Texas.

Baucus defended his work and urged his colleagues to “do our part to make quality, affordable health care available to all Americans.”

Baucus’ bill would help extend health insurance to an estimated 94 percent of Americans, including 29 million individuals who currently have none. An estimated 11 million people would join Medicaid under the legislation, and 25 million others would gain access to a new private-insurance exchange, including 7 million people who currently purchase their own plans or pay for expensive coverage through their employers.

Baucus said the cost of the bill would be near or below the $900 billion, 10-year target set by President Barack Obama.

Here are major revisions Baucus announced:

Families: Ease the financial burden on families with income up to four times the federal poverty level (about $88,000 a year for a family of four). In his original proposal, people making 133 percent to 400 percent of the federal poverty level could have been required to pay 3 percent to 13 percent of their income for insurance; the new proposal would lower that scale to 2 percent to 12 percent. Americans making less than 133 percent of the federal poverty level would qualify for Medicaid.

Penalties: Drop the maximum penalty for failing to comply with the insurance mandate from $3,800 per family to $1,900 per family.

Excise tax: Revise terms of an excise tax intended to help pay for the health-care overhaul and help control costs, exempting policies that cover high-risk workers such as firefighters and coal miners but increasing the tax rate from 35 percent to 40 percent.

Older consumers: Make insurance more affordable for seniors by limiting how much more insurers can charge them as compared with younger ones.

Medicaid: Allay fears that fiscally strained states would pay a larger health-care bill. The federal government would cover the full cost of expanding Medicaid in states with large Medicaid populations and fast-rising unemployment, such as California and Michigan.