Democrats are heaving a sigh of relief after a positive cost report on health care overhaul gave them a chance to rally around a Senate plan that significantly expands coverage while trimming the federal deficit.

The Congressional Budget Office said Wednesday that the latest version of the Senate Finance Committee proposal would expand coverage to 94 percent of all eligible Americans at a 10-year cost of $829 billion.

The budget umpires added that the legislation would reduce federal deficits by $81 billion over a decade and could lead to continued reductions in federal red ink in the years beyond.

But the middle-of-the-road plan still leaves about 25 million people uninsured when fully phased in, in 2019. Of those, nearly 17 million would be U.S. citizens or legal residents. Nearly 50 million U.S. residents now lack coverage.

The White House hailed the report as proof of what President Barack Obama has insisted all along. “The analysis confirms that we can provide stability and security for Americans with insurance and affordable options for uninsured Americans without adding a dime to the deficit — and saving money over the long term,” said spokesman Reid Cherlin.

Conservative Democrats were upbeat. Rep. Jim Matheson, D-Utah, a spokesman for the fiscally conservative Blue Dog Coalition, said he was encouraged that the Finance bill would cut the deficit and indicated that he’d like to see the House bill move in the same direction.

Republicans — with the exception of Maine Sen. Olympia Snowe — panned the Finance effort.

“A celebration of the deficit effects masks who pays the bills,” said Iowa Sen. Chuck Grassley of Iowa, the ranking Republican on the Finance Committee. “This package includes hundreds of billions of dollars in new taxes and fees. Most Americans with health insurance will see their premiums increase.”

Snowe, a member of the Finance Committee, told reporters she needs time to review the latest estimates. That the overall cost of the plan is lower than an earlier version is positive, she said.

The report clears the way for Finance to vote as early as next week on the legislation. Chairman Max Baucus, D-Mont., the principal architect of the measure, took to the Senate floor to announce the estimates within moments of receiving them.

“This legislation, I believe, is a smart investment on our federal balance sheet. It’s an even smarter investment for American families, businesses and our economy,” he said.

Finance is the fifth and last of the congressional panels to debate health care. The Baucus plan has a decided centrist flavor, shunning any provision for the government to sell insurance in competition with private industry. That provision, strongly favored by many Democrats and just as strongly opposed by Republicans, is still alive in proposed House versions of the legislation.

The Finance bill does not require businesses to offer coverage to their workers, either, although large firms that do not would be required to offset the cost of any government subsidies going to those employees.

While generally positive about the legislation’s effects, the budget office report contained important caveats.

One noted that the estimate does not include the costs of proposed payment increases for doctors serving Medicare patients, roughly $200 billion through 2019. Additionally, a so-called fail-safe mechanism to hold spending in line could result in cuts as large as 15 percent in federal subsidies designed to help the poor afford insurance, CBO said.

Beginning in 2013, Americans would be required to get health insurance, through an employer or a government program or by buying it themselves. Failure to obey the requirement would result in penalties of up to $750 per family.

The plan would set up a new insurance marketplace for consumers to compare and shop for a plan. Federal subsidies would be provided to millions of individuals and families to help defray the cost of coverage that would otherwise be out of their reach. The alternative to government-sold health care, a proposal for nonprofit co-ops that would compete with private companies, was judged largely ineffective by budget officials. Such arrangements “seem unlikely to establish a significant medical presence in many areas of the country,” they wrote.

The legislation also would ban current insurance industry practices that deny coverage on the basis of pre-existing medical conditions and restrict companies’ ability to charge vastly higher premiums on the basis of age, gender or other factors.

The measure would be paid for through a variety of tax increases and spending cuts, including savings of hundreds of billions of dollars from Medicare, the federal health care program for seniors.

Democratic leaders are hoping to hold votes on health care on the floor of the House and Senate within a few weeks.