(AP Photo/J. Scott Applewhite)

President Barack Obama and Republican House Speaker John Boehner spoke Tuesday after privately exchanging a new round of rival proposals for keeping the economy from tumbling off the "fiscal cliff" on Jan. 1, aides to both men told Yahoo News. The fresh discussion signaled a welcome bit of movement in negotiations that had appeared stalled for several days.

"The speaker and POTUS (the president of the United States) spoke by telephone this evening," a White House official said on condition of anonymity. A Boehner aide said the White House had presented a new offer on tax cuts and revenue increases on Monday and that Republicans had returned with a counter-offer on Tuesday.

The White House refused to offer details about its proposal. But the Boehner aide said the new offer brought Obama's initial demand for $1.6 trillion in new tax revenues down to $1.4 trillion.

The step would still require raising tax rates on wealthier Americans, something Boehner has previously rejected. Obama has said any final deal must raise tax rates on the richest Americans.

Boehner spokesman Michael Steel confirmed that the speaker's office had returned a counter-offer to the president but would not disclose many specifics.

"We sent the White House a counter-offer that would achieve tax and entitlement reform to solve our looming debt crisis and create more American jobs," Steel said.

Earlier Tuesday, the speaker himself complained that Obama hadn't been specific enough about the spending cuts he was prepared to embrace as part of a broader deficit-cutting plan.

"Let's be honest, we're broke," Boehner said on the House floor. "We're still waiting for the White House to identify what spending cuts the president is willing to make as part of the 'balanced approach' that he promised the American people."

Also Tuesday, Democratic Senate Majority Leader Harry Reid warned it was unlikely that lawmakers and the White House would be able to forge a compromise in time for Christmas, raising the prospect of a high-stakes game of chicken through the end of the year.

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"It's going to be extremely difficult to get it done before Christmas—but it could be done," the Nevada Democrat told reporters. "This is not something we can do easily, at least as far as bill drafting goes. But until we hear something from the Republicans, there's nothing to draft."

Reid's comments reflected the sense of gloom across the Capitol in recent days about prospects for averting automatic across-the-board tax hikes and painful government spending cuts that, together, could plunge the economy in a new recession. Those measures will take effect Jan. 1 unless Congress acts.

Obama had no public appearances Tuesday. His spokesman, Jay Carney, acknowledged the White House was deliberately being "incredibly opaque" about the behind-the scenes negotiations.

"If it weren't for the broader interest here, which is in trying to allow some space for the parties to see if they can achieve a compromise, you know, I'd be spilling my guts from here," Carney said.

At their weekly party lunch meetings on Capitol Hill, senators complained about the secrecy surrounding the talks.

Alabama Republican Sen. Jeff Sessions said Boehner "doesn't have my proxy" in cutting a deal with Obama.

"I've been elected, I've got a responsibility to make an independent determination of these matters," Sessions said.

Why the secrecy? Republican Sen. Rob Portman of Ohio told Yahoo News that "you need to build a level of trust first by not having it negotiated in the media."

"You need an opportunity, particularly with the president and Republican congressional leaders, to talk about some very tough issues," he said.

Still, Portman said, "they can't expect those of us who going to ultimately decide what happens in the Senate to vote on it without having a full understanding and input."

For Senate Budget Committee Chairman Kent Conrad of North Dakota, a Democrat who is retiring, the problem is less the back-room dealing and more the posturing for the cameras. "It's the same old lines over and over. How about just going into a room and getting a deal?" he said.

For his part, Republican Senate Minority Leader Mitch McConnell tried to steer the focus back to his party's preferred terrain: spending cuts. He listed a series of programs he considered wasteful, citing government promotion of a videogame that allows teens "to relive prom night."

"Get this: Taxpayers also just spent $325,000 on a Robotic squirrel named RoboSquirrel," he said. "The president seems to think that if all he talks about are taxes, and that's all reporters write about, somehow the rest of us will magically forget that government spending is completely out of control, and that he himself has been insisting on balance."

The Republican push came as party insiders privately acknowledged that they've placed themselves in a significant PR bind by insisting that tax cuts for middle class earners can only be extended if they are preserved for wealthier Americans as well. Obama wants to tax rates on income above $200,000 for individuals and $250,000 for families, a position Boehner and other Republican leaders have rejected.

"We're terribly weak on this, the tax component," one congressional Republican said.