Washington (CNN) -- The hotly contested tax deal negotiated by President Barack Obama and Republican leaders cleared a key Senate procedural hurdle Monday, with both parties strongly supporting a motion to end debate on the measure.
Final Senate approval could come as early as Tuesday on the package that includes extending for two years the Bush-era tax cuts set to expire December 31, as well as extending unemployment benefits for 13 months, cutting the payroll tax by 2 percentage points for a year and continuing a series of other tax breaks.
"This proves that both parties can, in fact, work together to grow our economy," Obama said of the 83-15 result, which took more than three hours to complete so that senators delayed by inclement weather could vote.
Anticipating final Senate approval of the measure, Obama urged the House to then pass it quickly despite misgivings by some House Democrats about specific provisions in the package.
"I recognize that folks on both sides of the political spectrum are unhappy" with parts of the deal, Obama said, calling it "the nature of compromise." Overall, he said, the measure will help bolster recovery from recession and provide taxpayers with certainty about what they will owe in 2011.
Senate Minority Leader Mitch McConnell, R-Kentucky, also heralded the broad support for the measure and warned the House against making any changes to score political points, saying that would kill the deal.
"If the House Democratic leadership decides to make partisan changes, they will ensure that every American taxpayer will see a job-killing tax hike on January 1st," McConnell said in a statement.
Disgruntled House Democrats, however, have warned that they may try to change the deal.
"What form the bill comes to the floor in is something that's under discussion and debate," Rep. Chris Van Hollen of Maryland, head of the Democratic Congressional Campaign Committee, said Sunday. In particular, Van Hollen questioned the value of an estate tax provision that some Democrats believe benefits the wealthy while doing little to aid the economy.
The estate tax -- currently scheduled to return in 2011 to a top rate of 55% along with a $1 million exemption -- would instead come back with a lower top rate of 35% along with a $5 million exemption under the deal.
Republican leaders argue that a full return of the estate tax would, among other things, make it nearly impossible for many family-owned small businesses to be passed down from one generation to the next.
In total, the tax and benefits package is expected to add $893 billion to the federal debt over the next five years, according to the nonpartisan Congressional Budget Office.
White House senior adviser David Axelrod ruled out any major changes to the tax package Sunday, telling CNN's "State of the Union" that it is time to move forward on a compromise that includes elements distasteful to each side.
Supporters of the compromise will ultimately prevail "because at the end of the day, no one wants to see taxes go up on 150 million Americans on January 1st," he said.
Two other House Democrats, Rep. Jim McDermott of Washington and Rep. Elijah Cummings of Maryland, agreed on "State of the Union" that the House would take up the package, even though some Democrats would vote against it.
Their remarks showed a softening in what has been sometimes vitriolic Democratic opposition to the package that Obama announced last week.
At a closed meeting Thursday at which members shouted "just say no," House Democrats decided against even considering the deal, raising questions about Obama's influence in his own party and whether any agreement with Republicans could win congressional approval in the current lame-duck session.
The tax cuts are set to expire at the end of the year, which means Obama and Democrats face a fast-approaching deadline to reach a deal or see tax bills increase for everyone.
With Republicans winning control of the House and diminishing the Democratic majority in the Senate in the new Congress that convenes in January, Obama and his top aides argue that a deal must be cut and delivered now.
House Democrats initially opposed the package because it includes a two-year extension of lower Bush-era tax rates for everyone, including millionaires. They support the stance Obama has championed for years: extending the current lower tax rates only for those earning up to $200,000 a year, or families earning $250,000, while letting rates for higher incomes return to 1990s levels.
However, Senate Republicans have refused to accept any proposal that allows tax cuts for the wealthy to expire, demanding that all current rates be extended. Last week, they blocked Democratic measures in the Senate to limit the extended tax cuts to income levels below $1 million a year.
At the same time, some conservatives are challenging the plan because of the deficit hit it would inflict.
Still, Sen. Dick Durbin of Illinois, the chamber's No. 2 Democratic leader, said McConnell had guaranteed that his caucus would permit the bill to come before the chamber.
"We will need Republican support to pass it" because of opposition by some Democrats, Durbin noted, adding that McConnell "has promised" that the support would be there.
CNN's Tom Cohen contributed to this report.