The Senate version is expected to pass at Monday afternoon's vote.
However, strong opposition in the House is threatening to derail Obama's carefully negotiated plan. The question isn't how many Democrats are against it, but who is for it.
The measure will extend Bush-era tax cuts, prevent large tax increases for nearly all Americans and keep jobless benefits flowing.
The plan's total cost by the latest congressional estimate is $857.8 billion over 10 years, which is pricier than the stimulus package.
Democrats have criticized the package as a tax giveaway to the rich.
"You can't give everybody a tax cut like it's Oprah Winfrey or Santa Claus," said Congressman Bobby Scott (D-Virginia). "Eventually, somebody is going to have to pay for it."
At the White House on Thursday, Obama got help from former President Bill Clinton who said, "I don't believe there is a better deal out there." All sides, he said, "are going to have to eat some things they don't like."
In the Senate, a rare spectacle occurred. Vermont's Bernie Sanders staged a symbolic filibuster, talking for hours upon hours against it.
"How can I get by on one house? I need five houses, 10 houses. I need three jet planes to take me all over the world," Sanders said. "Rich get richer. Middle class shrinks."
The Associated Press contributed to this report.