President Obama and White House officials underscored the need to compromise Monday in unveiling a congressional deal to avoid the expiration of the Bush-era tax cuts at the end of the year, but some of the toughest critics of Obama's version of compromise come from within his own party.

Democrats have generally argued that the tax cuts should be extended for the middle class -- but not for the wealthiest 2 percent. Republicans have argued that the cuts should be extended for all taxpayers.

The "framework" of the deal that Obama outlined Monday evening calls for a two-year extension of the cuts in all income tax brackets. It also would extend long-term unemployment benefits through next year. The estate tax rate would be renewed, but at a lower rate than even during the Bush administration. And the Obama administration is proposing a one-year payroll tax reduction that sources say would cut the amount contributed to Social Security from 6.2 percent to 4.2 percent.

"I have no doubt that everyone will find something in this compromise that they don't like," Obama said, but "we cannot play politics at a time when the American people are looking for us to solve problems." He said letting taxes increase for all Americans would create a chilling effect on the economy.

With Republicans set to take control of the House in January, Obama's remarks received a warm reception from the incoming speaker, House Republican Leader John Boehner.

"It’s encouraging that the White House is now willing to stop all of the job-killing tax hikes scheduled for January 1," Boehner spokesman Mike Steel said. "We look forward to discussing this proposal with House Republican members and the American people."

The top Democrat in the Senate, however, said much by not saying much at all. Majority Leader Harry Reid's office released a written statement on the tax deal saying only that Reid "plans on discussing it with his caucus tomorrow."

Obama, at his White House news conference Monday evening, renewed his calls for tax relief targeting the middle class and his criticism of making tax cuts for the wealthiest Americans permanent. But in the end, he said, a compromise must be reached, or tax hikes would make ordinary Americans "collateral damage for political warfare in Washington."

"I am not willing to let that happen," he said.

But some in his party caution a deal isn't done yet. Obama already is facing resistance from more liberal Democrats, who say the White House shouldn't give ground.

"We oppose acceding to Republican demands to extend the Bush tax cuts to millionaires and billionaires," Rep. Peter Welch, D-Vt., said in a letter to Speaker Nancy Pelosi. Obama "should not back down. Nor should we."

Beyond the Bush-era tax cuts, the renewal of the estate tax also could be tough to swallow for liberal Democrats, who have argued for higher rates. Under Bush, the tax on large estates dropped from 55 percent to 45 percent -- then to zero this year. Under the deal announced by Obama, it would change to 35 percent next year for estates larger than $5 million.

Sources tell Fox News that a payroll tax reduction, if approved, would take the place of the Obama-backed "Making Work Pay" tax credit that gave up to $400 to individuals and $800 to couples through the economic stimulus package. Obama had pressed for an extension of the tax credit, but Republicans objected.

Fox News' Chad Pergram and Trish Turner and Fox Business' Rich Edson contributed to this report.