Washington (CNN) -- The Senate approved a controversial $858 billion tax cut package Wednesday, overwhelmingly voting to extend the Bush-era tax reductions despite a series of objections from both the left and the right.

The measure passed 81-19 to advance to the House of Representatives, which will take it up on Thursday, according to Majority Leader Steny Hoyer, D-Maryland.

The package includes a two-year extension of the Bush-era tax cuts set to expire December 31. It also would extend unemployment benefits for 13 months, cut the payroll tax by 2 percentage points for a year, restore the estate tax at a lower level and continue a series of other tax breaks.

President Barack Obama praised the vote and urged the House of Representatives to quickly approve the bill, which the White House negotiated with Senate GOP leaders.

The Senate vote is "a win for American families, American businesses, and our economic recovery," Obama said in a written statement. "As this bill moves to the House ... I hope that members from both parties can come together in a spirit of common purpose to protect American families and our economy as a whole by passing this essential economic package."

House Democrats, however, have repeatedly warned that they may change the measure, particularly a provision dealing with the estate tax. Currently, the estate tax is scheduled to exempt inheritances up to $1 million and tax amounts above that at a rate of 55%. Under the tax package, it would be reduced to a rate of 35% on amounts above a $5 million individual exemption.

Conservatives 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. Liberals contend that a lower or nonexistent estate tax would merely benefit the wealthy while doing little to aid the economy.

A number of House Democrats, including Speaker Nancy Pelosi, D-California, want to change the estate tax to levels previously approved in a separate House bill that would exempt inheritances up to $3.5 million and tax amounts above that at a 45% rate. Pelosi said Wednesday the change would bring in an additional $25 billion instead of providing tax protection to only 6,600 more families through the lower rate and higher exemption in the negotiated tax deal.

However, more than two dozen moderate House Democrats submitted a letter to their House leadership Tuesday, calling for the tax package to be passed unchanged so it can go directly to Obama to be signed into law.

"This bipartisan compromise is by design a temporary measure and, with its passage, we must acknowledge that our work is not done," said the letter signed by 27 House Democrats as of Tuesday evening. "We must continue to work together in a bipartisan fashion -- with a sense of shared responsibility -- toward solutions that address our economic and fiscal challenges. It is time for us to put aside the partisan talking points and accomplish what the American people sent us here to do."

The House Rules Committee decided Wednesday night to allow a vote on changing the estate tax provision to the levels in the previously passed House bill. If approved, the changed bill would then go back to the Senate. If rejected, the House would then hold a separate vote on the Senate version, with approval sending the bill to Obama.

Republicans involved in the negotiations with the White House on the package have warned that any changes by the House could derail the entire proposal, causing tax rates to increase in 2011.

"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," Senate Minority Leader Mitch McConnell, R-Kentucky, said in a statement Monday.

With the Bush tax cuts set to expire at the end of the year, Obama and Democrats face a fast-approaching deadline to reach a deal. Republicans won control of the House and reduced the Democratic majority in the Senate in the new Congress convening in January, which would give Democrats less leverage to negotiate after the current lame-duck session.

House liberals are not the only ones objecting to the agreement. A number of conservatives, including likely 2012 GOP presidential candidate Mitt Romney, are challenging the deal because it doesn't permanently extend the Bush tax cuts and would add to the deficit.

CNN's Dana Bash, Tom Cohen, Alan Silverleib and Deirdre Walsh contributed to this report.