Senate Majority Leader Harry Reid indicated Thursday that the Senate Finance Committee will vote on its health care bill Tuesday morning. 

Congressional budget experts gave a boost Wednesday to that version of President Obama's proposed overhaul of the health care system, concluding that the bill pending in the Finance Committee would cost $829 billion over the next 10 years -- under the $900 billion target set by Obama.

The preliminary report, released Wednesday by the non-partisan Congressional Budget Office, also said the committee's health care reform package will not add to the national deficit -- and will save $81 billion over the next 10 years compared to current federal health care spending.

But the political battle over how to interpret the CBO's report may have only begun.

"Our balanced approach to health reform has paid off yet again with the news today that the America's Healthy Future Act remains fully paid for, begins to reduce the federal deficit within 10 years and makes significant reductions in federal debt over the next several decades," said Sen. Max Baucus, the chairman of the Senate Finance Committee the key negotiator behind the legislation.

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

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

And Senate Minority Leader Mitch McConnell said the Finance Committee bill wasn't viable anyway and "will never see the Senate floor."

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 CBO report estimated that the bill would reduce rolls of uninsured by 29 million over the next 10 years -- ensuring that 94 percent of Americans will be covered.

The report paves the way for the Senate Finance Committee to vote as early as Friday on the legislation, which is largely in line with President Obama's call for the most sweeping overhaul of the nation's health care system in a half-century.

Congressional tax experts say the proposed legislation would require health care industries to pay $121 billion in taxes over 10 years -- about $29 billion more than originally thought.

Finance Committee Republicans have been arguing the measure contains too many new taxes.

Grassley blasted the bill on Wednesday, saying, "It's going to be a very costly bill."

"If you take the years 2013 through 2023, you'll find that it's a very very expensive bill," he said.

The committee's proposal, which calls for co-ops instead of a so-called "public option," has to be blended with the version approved by the Senate Committee on Health, Education, Labor, and Pensions, which does include the public option. Only then can it be considered by the full Senate.

Senate Majority Leader Harry Reid will face a difficult task in merging the two bills into one -- and presumably one that includes the government-run insurance plan that he and other liberal Democrats have steadfastly backed.

The Finance committee voted last week to strike two amendments that would establish a government-run insurance plan to compete with private insurance coverage. But the bill created in July by the Health Committee includes a public option and requires employers to offer insurance to their employees. 

The question over whether Reid will push for a government-run insurance plan in the final legislation remains to be answered. Reid has said a public option is essential to reform, and other leading Democrats like House Speaker Nancy Pelosi have stressed its importance in expanding coverage to the millions of uninsured.

"Today‚Äôs news from the Congressional Budget Office on the Finance Committee's bill is another important step down the road toward enacting comprehensive health insurance reform," Reid said.  "I look forward to the Finance Committee completing its work as soon as possible. After the committee acts, we must begin the important work of merging their proposal with the HELP Committee legislation. We'll work with the White House and the chairmen of the HELP and Finance Committees to craft a bill that can garner 60 votes." 

The final Senate bill will then go up against the House version, which includes a government-run insurance option to compete with private insurers.

Chairman of the House Ways and Means Committee, Rep. Charles Rangel, D-N.Y., said he intends to submit the House health care reform bill to the CBO by Friday. 

House Democrats are expected to discuss potential "pay-fors" in their health care reform bill on Thursday, congressional aides told FOX News.

"Everything will be done by tomorrow," Rangel said.

FOX News' Trish Turner and the Associated Press contributed to this report.