'Fiscal Cliff' Impasse: Can a Deal Still Get Done?

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With negotiations on a "fiscal cliff" deal at an impasse, Democrats and Republicans have turned toward sending political messages just before the Christmas holidays.

The Republican-controlled House has scheduled a vote later Thursday on what Speaker John Boehner calls "Plan B"—a bill to allow tax rates to rise back to Clinton-era levels only on family incomes above $1 million per year. (Read More: House to Vote on Plan B as Hopes for 'Cliff' Deal Fade .)

Because many Republicans oppose raising taxes on anyone, Boehner has added a vote on separate legislation to cut spending by $200 billion as a means of luring recalcitrant conservatives.

House Majority Leader Eric Cantor labeled the measures the only "concrete action" to avert the fiscal cliff and challenged Democrats to enact them.

Democrats have no intention to. Senate Majority Leader Harry Reid said the measure cannot clear the Senate, and the White House said President Barack Obama would veto Plan B even if it did pass.

That suggests Congress will leave Washington for the weekend with the issue unresolved, then return next week with only days to go before the Dec. 31 deadline. (Read More: Could a 'Fiscal Cliff' Deal Include Cap on the AMT? )

To increase pressure on Republicans, the White House summoned a group of Washington business lobbyists Wednesday evening to enlist their assistance.

One participant in the meeting said the message from White House officials was the negotiations had soured but Obama doesn't want to give up and go over the cliff. (Read More: Fitch Warns US Could Lose AAA If 'Fiscal Cliff' Hits.)

The participant speculated that a decision by House members and senators would give Obama and Boehner more breathing room to negotiate privately over the weekend with the goal of presenting members with a deal when they return next week.

But that's no guarantee both chambers could pass such a deal, and some White House and congressional officials have grown significantly gloomier in recent days about the prospect of a bipartisan solution.

—By CNBC's John Harwood; Follow him on Twitter: @JohnJHarwood