While also setting the estate tax at 35% for two years on inheritances worth more than $5 million, a senior Democratic source told CNN.
The deal also includes a temporary 2 percentage-point reduction in the payroll tax to replace Obama's "making work pay" tax credit from the 2009 economic stimulus package for lower-income Americans, the senior Democratic source said.
The White House announced Obama would make a statement to reporters on the issue Monday evening. It was unclear if the hastily arranged statement by Obama signaled that congressional Democrats, especially liberal House Democrats, had accepted the proposal.
As proposed, the deal would add trillions of dollars to federal spending in coming years by extending the lower tax rates as well as the jobless benefits at a time when Obama, Republican leaders and a federal deficit commission appointed by the president all say that the growing federal debt must be brought under control.
The senior Democratic source said the proposed deal would prohibit amendments by either party. An administration source familiar with the talks said the one-year reduction of the payroll tax would bring savings of about $1,000 for someone making $50,000.
House Democrats, who have approved a measure extending the Bush-era tax cuts for family incomes up to $250,000 a year, indicated earlier Monday they were unhappy with the negotiations that the White House was conducting with congressional Republicans.
"We won't rubber stamp a deal between the White House and (Senate Minority Leader) Mitch McConnell," one Democratic congressional source told CNN. "We want to make it clear. Don't take our support for granted."
House Speaker Nancy Pelosi, D-California, and Majority Leader Steny Hoyer, D-Maryland, were among Democratic leaders who attended a White House meeting with Obama and Vice President Joe Biden to discuss the proposed deal.
According to the senior Democratic source, Obama and Biden told the congressional Democrats that the proposed deal was the best they could expect.
Liberal House Democrats are believed to be among the most reluctant in Congress to agree to a deal extending all of the 2001 and 2003 tax cuts.
The House measure, which was blocked from consideration in the Senate by a Republican filibuster, would cause tax rates to increase to 1990s levels for individuals making more than $200,000 a year and families earning more than $250,000. Senate Republicans blocked a similar proposal that set the income threshold for higher tax rates at anything over $1 million.
Top senators from both parties had indicated Sunday that a deal linking the extension of lower tax rates for everyone with extended unemployment benefits was likely. Congress would continue working on a long-term plan to reduce the nation's debt.
Democrats contend the nation must prevent working-class Americans from facing higher taxes, as promised by Obama in his 2008 election campaign, but can't afford the extra hundreds of billions of dollars it would cost to maintain the tax cuts for the wealthy. Republicans argue that the economy remains too weak to allow anyone's taxes to increase.
Earlier Monday, Obama reiterated his position that extending the cuts for the wealthiest Americans would be fiscally irresponsible, and stressed the opinion of Democratic leaders that an extension of unemployment benefits needs to be part of any agreement with the GOP.
"We have got to find consensus here because a middle-class tax hike would be very tough, not only on working families, it would also be a drag on our economy at this moment," Obama told an audience in Winston-Salem, North Carolina.
"We've got to make sure that we are coming up with a solution even if it is not 100% of what I want or what the Republicans want," he said.