By JANET HOOK, JONATHAN WEISMAN and PATRICK O'CONNOR

WASHINGTON—President Barack Obama's tax-cut compromise with Republicans was greeted with anger from fellow Democrats in Congress Tuesday, but many seemed resigned to accepting it as the best deal they could get and a step toward reviving the weakened economy.

Democrats criticized the broad tax package for cutting taxes on high earners and setting tax rates too low on large inheritances, as well as for its effect on the country's budget deficit. But Democrats also said they didn't yet see a revolt spreading so far that it would derail the agreement in the Senate. Prospects for passage are more uncertain in the House, where many liberal members are balking at planned changes to the estate tax.

President Obama's proposed deal with Republican leaders in Congress to extend tax cuts for two years is already catching plenty of criticism within his party, as Democrats prepare to debate the plan. Jerry Seib has details from Washington.

With Republicans praising the tax package, the administration began an intense drive to sell the deal to the president's own party. In testy tones, Mr. Obama used a press conference to tell Democrats this was the best deal he could strike. Vice President Joe Biden was dispatched to Capitol Hill, where he warned lawmakers of economic and political consequences should the deal collapse.

Mr. Obama said that he still opposed the centerpiece of the deal—a two-year extension of Bush-era income tax cuts for all Americans—but that Republicans had "held hostage" the cuts he wanted for middle-class families to ensure cuts for the wealthy. "I have not been able to budge them...and in the meantime, there are a whole bunch of people being hurt" by the political stalemate, Mr. Obama said.

Mr. Obama said the tax package "will make a real difference in the pace of job creation and economic growth. In other words, it's a good deal for the American people."

A Look at the Deal and What It Would Means to Taxpayers

The bipartisan tax agreement announced Tuesday addresses a range of tax issues that have been in question for months or years. While there isn't yet any legislation or comprehensive outline of the deal's components, here are provisions under discussion.

After hearing from Mr. Biden on Capitol Hill, Senate Budget Committee Chairman Kent Conrad (D., N.D.) said he was shelving deep reservations about the agreement adding to the deficit and would back the bill. "I am prepared to support this, because overall it is necessary," Mr. Conrad said. He foresaw no major obstacles to the agreement's passage in the Senate.

Sen. Mary Landrieu (D., La.) said the extended tax cuts for upper-income Americans amounted to "almost moral corruptness," but that those objections weren't enough to put her in the "no" column yet.

On the Republican side of the aisle, Senate Minority Leader Mitch McConnell (R., Ky.) said he believed "the vast majority" of GOP senators would vote for it. Sen. Joe Lieberman (I., Conn.), said he was confident the deal would pass the Senate.

Passions ran higher in the House, where the Democratic caucus is more liberal and opposition is strong to allowing the upper income brackets to be continued at current levels. Liberals were especially outraged by Obama's decision to accept a GOP estate-tax proposal that critics believe is too generous to people with large inheritances.

"It isn't just the progressive caucus. Democrats in general were really upset," said Rep. Lynn Woolsey (D.,Calif.), who said Democrats at a White House Christmas party Monday night were "toasting to the billionaires—very sarcastically."

Mr. Biden will meet with the House Democratic Caucus Wednesday. Angry liberals, after a Tuesday evening party caucus, said the administration couldn't count on their support.

"I don't think that the president can count on the support of House Democrats to pass this package," said Rep. Anthony Weiner (D., N.Y.).

Obama reached a deal with GOP Congressional leaders on a broad tax package that would extend the Bush-era tax cuts for two years, reduce payroll taxes for one year and set the estate tax at 35%. Jonathan Weisman, Bob O'Brien and David Weidner discuss. Also, Martin Vaughan discusses what the tax cut plan mean for you.

Some elements of the deal are still being nailed down, and Democratic aides said sweeteners might be added to make the bill more palatable to hesitant lawmakers. But Mr. McConnell, a principal architect of the deal, called it "essentially final."

The framework, announced by Mr. Obama Monday after weeks of talks with congressional Republicans, includes the two-year extension of income-tax cuts signed into law by President George W. Bush.

Without action, those tax cuts are due to expire at year's end. Mr. Obama wanted them extended only for couples earning up to $250,000, saying the cost to extend them for the wealthiest Americans was too high.

Republicans said they wanted them extended for everyone, and that no one's taxes should rise while the economic recovery is weak.

The deal includes a 13-month extension of lapsed federal jobless benefits, providing up to 99 weeks assistance to the long-term unemployed in states hit the hardest by the downturn.

In a concession to Republicans that surprised many Democrats, the deal also restores the estate tax at a 35% rate for two years and applies it only to estates over $5 million. The estate tax has been eliminated for this year and was due to be revived in 2011 at a rate of 55% on estates over $1 million.

Some Democrats in the House are pushing to lower the threshold from $5 million to $3.5 million and raising the tax to 45% from 35%.

"If this is the playbook for the next two years, we want out because Democrats in the House are irrelevant," said New Jersey Rep. Bill Pascrell. He said the president "made a mistake" in agreeing to the deal.

The agreement also includes a two-percentage-point payroll-tax reduction, lowering Social Security taxes for most Americans to 4.2% from 6.2% for one year. And it would extend a raft of other tax cuts aimed at middle-class taxpayers, including a two-year fix to ensure that most Americans are shielded from the Alternative Minimum Tax.

While Republicans generally embraced the agreement, conservatives such as Sens. Jim DeMint (R., S.C.) and Tom Coburn (R., Okla.) were dismayed that the tax package wouldn't require spending cuts to cover the cost of extending unemployment benefits.

Faced with the restiveness in his own ranks, Mr. Obama in his press conference Tuesday said he made the deal because he was faced with a stark choice: Give Republicans what he called their "holy grail"—the income tax cuts for the wealthy—or risk a major economic blow to the U.S. economy and to "real people" with real economic struggles.

"It is tempting not to negotiate with hostage-takers, unless the hostage gets harmed. Then, people will question the wisdom of that strategy," he said. "In this case, the hostage was the American people, and I was not willing to see them get harmed."

In the face of Democratic criticism, Mr. Obama showed a rare flash of anger, choosing to browbeat opponents in his party rather than cajole them.

He said criticism of the tax package reminded him of the carping he faced during the health-care debate, when many on the left fixated on the inability to create a government-run health-insurance option instead of lauding an expansion of health-insurance coverage to 30 million people.

"If that's the standard by which we are measuring success or core principles, then, let's face it, we will never get anything done," he snapped. "People will have the satisfaction of having a purist position and no victories for the American people."

In this case, he argued, middle- and lower-income families would benefit from the payroll-tax reduction, the extended jobless benefits and other elements of the deal, and that the package overall would stimulate job growth and the economy.

—Corey Boles and Alan Zibel contributed to this article