President Obama hastily scheduled an afternoon press conference at the White House Tuesday, seeking to head off growing anger in his own party over compromises to Republicans in a tax cut deal announced Monday.

The press conference was announced less than two hours in advance as House Democratic leaders presented a united front in opposition to the deal as it currently stands, and anger among the Senate Democrat rank and file became more evident.

Vice President Joe Biden, meanwhile, attended the weekly lunch for Senate Democrats, seeking to call on the relationships he built during a 36-year career in the Senate to build support for the deal.

A noon statement by House Speaker Nancy Pelosi on the tax deal, nearly 24 hours after she was briefed on it at the White House Monday afternoon, expressed clear dissatisfaction with the preliminary deal between Obama and congressional Republicans.

Most specifically, Pelosi voiced the anger of many on the left about extending the current tax rates for those making more than $250,000 and for allowing the estate tax to move from its current one-year level of zero percent to 35 percent instead of 55 percent, as it is scheduled to do.

“We will continue discussions with the President and our Caucus in the days ahead,” said Pelosi, California Democrat.

“The Republican demands would provide tax cuts to the millionaires and billionaires, fail to create jobs and increase the deficit. And to add insult to injury, the Republican estate tax proposal would help only 39,000 of America’s richest families, while adding about $25 billion more to the deficit,” Pelosi said.

A Senate Republican aide acknowledged that while there may be plenty of discontent on the right about the fact that the deal would add roughly $600 to $900 billion to the deficit, they expect to get support from most of their 42 senators.

House Democrats, the Republican said, “are the real wild card right now. It’s clear that the White House has some work to do.”

Despite the protests from House Democratic leaders, the pressure on them to pass a deal without allowing taxes to go up is immense given the electoral and political consequences of letting the cuts expire.

And if a deal is reached soon enough, Congress can try to move forward on other matters of importance to the White House and the Democratic base, such as ratification of a nuclear arms reduction treaty with Russia, a repeal of the military’s “Don’t Ask, Don’t Tell” policy, and the DREAM Act.

Nonetheless, in a briefing with reporters Tuesday morning, House Majority Leader Steny Hoyer, Maryland Democrat, voiced concern with the the deal as it now stands, calling the compromise “contradictory” and said he expects the Senate to move before the House.

“It’s not good policy,” he said.

“At a time when the deficit is at unacceptable levels, giving tax cuts to high income Americans is not appropriate. Bringing the deficit down is a principle objective,” he said. “On the other hand, raising taxes on middle income Americans is not appropriate either.”

Hoyer defended his party’s decision last week to hold a vote on whether to permanently extend the tax rates only to individuals earning less than $200,000 per year and married couples with incomes below $250,000. The measure passed, but was later rejected by the Senate. He also said that there was “no consensus or agreement” with the White House in yesterday’s meeting with House leaders.

“We have been very clear on our position,” he said.

Democratic Caucus Chairman Rep. John Larson of Connecticut said Obama’s plan would be “difficult” to sell to the caucus and that he is open to ideas from his party on altering the plan.

And Rep. Chris Van Hollen, the Maryland Democrat and member of party leadership who represented the House Democrats in the tax cut negotiations, said on Bloomberg Television that he had “serious reservations” about the package.

“There are components that the Republicans got that probably should not have been in this package,” Van Hollen said, listing the estate tax rate as the most objectionable issue.

In the Senate, reports grew that Democrats were angry over the numerous concessions made to the GOP, and over the fact that Obama negotiated so directly with Republicans without keeping his own party in the loop.

“To me at has a bad aroma, and I don’t like what I see,” said Sen. Frank Lautenberg, New Jersey Democrat. “I think capitulation under pressure is something that just has, in my view, the wrong message and I believe will have the wrong outcome.”

The outcry from the liberal grassroots continued Tuesday as well, as speculation among some on leading blogs moved to what Obama will do on Social Security in the coming months.

“Does Obama have any core principles he won’t sell out? Is even Social Security safe?,” wrote Markos Moulitsas, founder of DailyKos.com, on his Twitter feed.

And some on the right also found plenty to be dislike in the plan.

“There will be very little economic boost from this deal,” wrote Daniel Mitchell of the libertarian Cato Institute. “As mentioned above, people generally don’t increase output in response to short-term provisions.”

“I worry that this will undermine the case for lower tax rates since observers may conclude that they don’t have much positive effect.”

Rep. Michele Bachmann, the firebrand conservative Republican from Minnesota, said Monday that she was not sure she would support any deal with an unpaid for, 13-month extension of unemployment insurance.

“I don’t know that Republicans would necessarily go along with that vote. That would be a very hard vote to take,” she said on Sean Hannity’s radio show.

But there was positive reaction on the tax cut deal from some portions of the left.

John Podesta, president and CEO of the liberal Center for American Progress, said that while the concessions Obama made were “a steep price” to pay, the compromise was necessary.

“This deal will mean about 2 million jobs saved or created over the next two years. On balance, I think the President was right to choose helping working Americans over a December conflagration,” Podesta said.

But Podesta, a former White House chief of staff to President Bill Clinton, did say that he is worried about Obama’s ability to negotiate more skillfully in the future with an aggressive and emboldened GOP.

“The question hanging over Washington and the country today is how will [Obama] avoid repeating the same scenario being played out again and again for the next two years? That’s a question that is keeping me awake at night,” Podesta said.

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Laura Donovan contributed to this report.