Washington (CNN) -- The Senate health care bill cleared a third and final procedural hurdle Wednesday as Democrats successfully limited remaining debate time on the $871 billion measure.

The Senate voted 60-39 along party lines to set up a final vote on the bill early Thursday morning.

Democrats also turned back last-ditch motions from Republicans claiming various provisions in the bill, including a mandate that individuals purchase coverage, are unconstitutional.

"It's long past time we declare health care a right and not a privilege," Senate Majority Leader Harry Reid, a Nevada Democrat, said after the vote.

"Today is a victory ... for American families," proclaimed Sen. Max Baucus, D-Montana. "Americans won."

The expected victory for President Obama's top domestic priority comes after nearly a year of sharply polarized deliberations on Capitol Hill. Any measure passed by the Senate, however, will still have to be merged with a $1 trillion plan approved by the House of Representatives in November.

Increasingly confident Democrats hope to have a bill ready for Obama's signature before his State of the Union address early next year.

"Health care reform is not a matter of if," White House Press Secretary Robert Gibbs said Tuesday. "Health care reform now is a matter of when."

If a combined House-Senate health care bill clears Congress and is signed by Obama, it would be the biggest expansion of federal health care guarantees since the enactment of Medicare and Medicaid over four decades ago.

Republicans have mounted a no-holds-barred legislative campaign against the bill, using a series of procedural maneuvers to slow debate while arguing that the measure will raise taxes while doing little to slow spiraling health care costs.

They've also ripped Senate Majority Leader Harry Reid, D-Nevada, for garnering the 60 votes necessary to pass the bill in part by cobbling together a series of "sweetheart deals" for wavering members of the Democratic caucus.

"This bill is a grab bag of Chicago-style, backroom buyoffs," Utah GOP Sen. Orrin Hatch said Wednesday.

Recent compromises made to win the backing of moderates such as Sen. Ben Nelson of Nebraska and Sen. Joe Lieberman of Connecticut also angered many liberal Democrats and threatened to undermine support for the bill.

Democrats have now held three key procedural votes on the health care bill this week. The backing of all 60 members of the Democratic caucus was required during each vote in order to overcome a filibuster from a GOP minority united in opposition.

Final passage of the measure, in contrast, will require only a bare majority in the 100-member chamber.

Enthusiastic top Democrats argue the Senate bill would constitute a positive change of historic proportions. The legislation, according to the nonpartisan Congressional Budget Office, would extend health insurance to more than 30 million Americans currently lacking coverage while reducing the federal deficit.

The House and Senate bills agree on a broad range of changes that could impact every American's coverage.

Among other things, they have agreed to subsidize insurance for a family of four making up to roughly $88,000 annually, or 400 percent of the federal poverty level.

They also have agreed to create health insurance exchanges designed to make it easier for small businesses, the self-employed and the unemployed to pool resources and purchase less-expensive coverage. Both the House plan and the Senate bill would eventually limit total out-of-pocket expenses and prevent insurance companies from denying coverage for pre-existing conditions.

Insurers also would be barred from charging higher premiums based on a person's gender or medical history. However, both bills allow insurance companies to charge higher premiums for older customers.

Medicaid would be significantly expanded under both proposals. The House bill would extend coverage to individuals earning up to 150 percent of the poverty line, or roughly $33,000 for a family of four; the Senate plan ensures coverage to those earning up to 133 percent of the poverty level, or just over $29,000 for a family of four.

Major differences between the bills will be the focus of the conference committee that will try to merge them. House and Senate Democrats are still divided over how to pay for their plans. They are also split on, among other things, language relating to abortion coverage and whether to include a government-run public health insurance option.

The House bill includes a public option; the more conservative Senate measure would instead create nonprofit private plans overseen by the federal government.