House Democrats won't be willing to "drive off a cliff" in the tax debate, their party's chairman said Friday.

Democratic National Committee (DNC) Chairman Tim Kaine called the bluff of recalcitrant congressional Democrats who have vowed to vote against the tax cut compromise proposed earlier this week by President Obama.

"I don't think they're willing to drive off a cliff, because no one wants to get to Jan. 1 and see anyone get hurt," Kaine said on "The Early Show" on CBS.

Obama's faced a revolt in Congress by members of his own party, who have griped that his tax-cut deal makes too many concessions to Republicans, concessions they argue that Obama made too quickly.

The White House and the DNC have launched an all-out effort to sell the tax cuts and create momentum for their passage by the end of the lame-duck Congress, since the tax rates would spring up at the beginning of next year without congressional action.

Kaine's been willing to serve as an enforcer of loyalty to the president over the past two years in his capacity as DNC chairman. At the height of the campaign season, when a number of endangered incumbents were looking to distance themselves from Obama, Kaine went out and warned Democrats that they were making a big mistake.

"You see the House doing what a legislative body always will," Kaine said of lawmakers' action on taxes. "But the framework is a set one; we've got to make these tax policies stick."

The DNC chairman said he thought there was "virtually no chance" that congressional Democrats would let taxes go up come Jan. 1.