The U.S. House of Representatives will reconvene on Sunday as the end-of-the-year deadline for the fiscal cliff looms, sources told CNN on Sunday.

Senate leaders argued Thursday over how even to debate a possible fiscal agreement, four days before the deadline for a deal to avoid automatic tax hikes and spending cuts set to take effect in the new year.

The back-and-forth occurred as President Barack Obama and the Senate returned to Washington after a Christmas break, and House leaders announced the chamber would reconvene on Sunday for what will be the final days of the 112th Congress, before a new legislature is sworn in next week.

Republicans insisted on more details about a scaled-back proposal first mentioned last Friday by President Barack Obama, with Senate GOP leader Mitch McConnell saying his side won't "write a blank check for anything Senate Democrats put forward just because we find ourselves at edge of the cliff."

A Senate Democratic leadership member also said more details would be provided, but two White House officials said Obama will not send a fiscal cliff measure to Congress.

Senate Majority Leader Harry Reid, D-Nevada, argued it was Republicans who undermined an agreement by refusing to compromise on their opposition to higher tax rates for the wealthy.

"We are in same situation we've been in for a long time," Reid said of what he described as GOP intransigence that prevented progress on deficit reduction for the past two years. "We can't negotiate with ourselves."

Economists warn the full impact of the fiscal cliff could spark another recession. In signs of the potential effect, the Consumer Confidence Index sank.

Last week, Obama called for a scaled-back plan that would prevent tax increases on middle-class Americans and extend unemployment benefits.

McConnell told Obama in a telephone conversation Wednesday that he must see details of a proposal before he can figure out any process for a Senate vote.

However, a senior Democratic Senate source told CNN on Thursday that it was McConnell who must first work things out with House Speaker John Boehner on how legislation will proceed before Democrats provide more details of their plan.

Hopes for a so-called grand bargain that would address the nation's chronic federal deficits and debt appeared dashed for now, leaving it to the White House and legislators to work out a less ambitious agreement.

The principal dispute continues to be over taxes, specifically the demand by Obama and Democrats to extend most of the tax cuts passed under President George W. Bush while allowing higher rates of the 1990s to return on top income brackets.

Obama campaigned for reelection on keeping the current lower tax rates on family income up to $250,000, which he argues would protect 98% of Americans and 97% of small businesses from rates that increase on income above that level.

Republicans oppose any kind of increase in tax rates, and Boehner suffered the political indignity last week of offering a compromise -- a $1 million threshold for the higher rates to kick in -- that his colleagues refused to support because it raised taxes and had no chance of passing the Senate.

With House Republicans unable to resolve the impasse, the focus shifted to the Democratic majority in the Senate to come up with a way forward that could pass the House and get signed into law by Obama.

Last Friday, the president proposed the scaled-back agreement that included his call for extending tax cuts on households with incomes under $250,000, as well as an extension of unemployment insurance.

Little if any negotation occurred since then, and Reid expressed doubt Thursday that enough time remained to reach an agreement.

"I don't know, time-wise, how it can happen now," he said as he opened the Senate's first session back from the holiday.

Possible scenarios include a short-term deal now, setting up continued negotiations next year when Obama and a new Congress that convenes in January confront a need to raise the federal debt ceiling and approving further spending to keep the government funded.

Another possibility would be a short-term deal reached after January 1 that would change the political calculus by having legislators vote for cutting the higher tax rates from the fiscal cliff -- a much more palatable exercise than the current debate over allowing top rates to increase.

Retiring Republican Rep. Steve LaTourette of Ohio told CNN on Thursday that such an outcome would be entirely due to politics.

"Nobody is willing to pull the trigger" on an agreement because "everybody wants to play the blame game," he said. "This blame game is about to put us over the edge."

In his remarks Thursday, Reid said Boehner wanted to wait until after the new House re-elects him as speaker on January 3 before proceeding with a compromise that will need support from Democrats as well as Republicans in order to pass.

Boehner was "more concerned about his speakership than putting the country on firm financial footing," Reid charged.