House Majority Leader Steny Hoyer said he had "no consensus or agreement reached by House leaders" concerning the deal Obama negotiated with the GOP, The Hill said.
Among other things, the agreement would extend all of the tax rates enacted during George W. Bush's presidency for two years, extend unemployment benefits for 13 months and cut the payroll tax by 2 percent through the end of next year.
Speaker Nancy Pelosi, D-Calif., already on record as opposing extending lower tax rates for the wealthiest taxpayers, also criticized GOP provisions in the agreement.
Democrats wanted to extend the tax cuts for the middle class but let the rates increase for individuals with incomes above $200,000 and households with incomes above $250,000 to the level they were at before the cuts were enacted.
Pelosi said in a post on her Twitter page the GOP provisions in the tax proposal would add to the deficit, benefit the rich and not create jobs.
Pelosi said later in a statement, "We will continue discussions with the president and our caucus in the days ahead. ... Democratic priorities remain clear: to provide a tax cut for working families, to promote policies that produce jobs and economic growth, and to assist millions of our fellow Americans who have lost their jobs through no fault of their own."
During his weekly news conference, Hoyer reiterated Democratic opposition to extending tax rates for the wealthy, saying House leaders would discuss the deal with the Democratic caucus "over the next few days."
"We'd like the Senate to move first on this issue," Hoyer told reporters.
While stopping short of saying House Democrats would demand changes to the proposal, Hoyer noted, "It's got to pass both houses."
Hoyer lauded the payroll tax reduction included in the deal but criticized the plan to set the estate tax at 35 percent for individuals bequeathed more than $5 million.
"I'm not happy with that. It will cost substantial dollars," Hoyer said of the estate tax proposal.
Vice President Joe Biden will meet Tuesday with Senate Democrats on Capitol Hill, hoping to draw on his long personal relationships with many of his former colleagues to soothe angry reaction to the deal cut by the White House on tax cuts Monday.
Criticism wasn't limited to House Democrats, The Washington Post reported.
Sen. Bernie Sanders, Ind-Vt., called the deal an "absolute disaster."
Sen. Sherrod Brown, D-Ohio, also said he was "not at all happy" with the deal. Retiring Sen. George Voinovich, R-Ohio, said he wouldn't support any compromise with an extension of the Bush tax cuts.
Notable deaths of 2014 [PHOTOS]