WASHINGTON (CNN) -

President Barack Obama spoke separately Friday with Speaker John Boehner and the top Senate Democrat to try to salvage a fiscal cliff deal by the end of year, after Republican disarray in the U.S. House put the negotiations in limbo.

In a previously unscheduled statement to reporters, Obama outlined a possible agreement that he said would include protecting middle-class Americans from a tax hike, extending unemployment benefits and setting a framework for future deficit reduction steps.

He called on Congress to pass the agreement after a Christmas break so he can sign it before the end of the year, when the fiscal cliff arrives in the form of automatic tax increases and deep spending cuts.

"Laws can only pass with support from Democrats and Republicans," Obama said in urging both sides to compromise.

The president planned to fly with his family to Hawaii on Friday night for the holiday and return to Washington after Christmas, while House and Senate members also headed home with plans to return on December 27 if needed.

Boehner's spokesman said the speaker will be "ready to find a solution that can pass both houses of Congress" when he returns to Washington.

While congressional leaders continued to bicker Friday over the next step, the president's phone discussion with Boehner and a White House meeting with Senate Majority Leader Harry Reid signaled an attempt to provide the nation and investors with hope that an agreement can be reached.

An aide to Reid said the short-term proposal to avoid the fiscal cliff should include extending tax cuts for middle-class families and unemployment insurance while delaying the automatic spending cuts set to take effect in the new year.

Obama acknowledged what had become obvious: the broader deficit reduction deal he seeks will likely come in stages, rather than in the so-called grand bargain he and Boehner have been negotiating.

The main issue of disagreement continued to be taxes, specifically whether rates should go up on top income brackets for the wealthiest Americans as part of an agreement to reduce the nation's chronic federal deficits and debt.

Without a deal, the fiscal cliff could trigger a recession, economists warn. Stocks closed down sharply on Friday over the latest impasse in the deficit talks, a sign of investor fears of a slowdown as the nation slowly continued to emerge from recession.

Earlier Friday, Reid called for House Republicans to quickly approve a Senate plan championed by Obama that would extend tax cuts for family income up to $250,000 while allowing rates to return to higher levels of the 1990s above that threshold.

His Republican counterpart, Sen. Mitch McConnell of Kentucky, responded that the Senate should instead take up a House Republican measure extending the tax cuts for everyone as a temporary move before negotiations next year on broader tax reform.

The GOP revulsion over any kind of tax rate increase has stymied deficit negotiations for two years and led to unusual political drama, such as McConnell recently filibustering his own proposal and Thursday night's rebuff by House Republicans of an alternative tax plan pushed by Boehner, their leader.

Boehner said at a news conference Friday that his Republican colleagues refused to back his plan, which would have extended all tax cuts except for income over $1 million, because of fears of being blamed for a tax increase.

"They weren't taking it out on me," he said. "They were dealing with the perception that somebody might accuse them of raising taxes."

The lack of backing by his own caucus was a political blow to Boehner and raised more questions than answers about what happens next in the tough negotiations with Obama on either a broad deficit reduction agreement or a smaller step to avoid the fiscal cliff.

A senior Democratic Senate source said scenarios under consideration by the party include trying to work out short-term or comprehensive agreements now, or going into next year -- and over the fiscal cliff -- without a deal to quickly pass a compromise plan in the new Congress that convenes on January 3.

Waiting until next year would make the vote a tax cut from the automatic higher rates that will take effect under the fiscal cliff, instead of the current situation of extending some cuts and having top rates go up, the source noted.

In addition, Democrats will have two more seats in the new Senate and a stronger House minority, as well as increased pressure on Republicans to keep taxes low on middle class Americans, according to the source.

Trying to hammer out a deal now means working with limited time and stronger Republican contingents in both chambers, the source said.

Boehner made clear Friday that the negotiations with Obama on a broad deficit reduction agreement hit an impasse this week when both sides offered their "bottom line" positions that included major concessions -- but remained a few hundred billion dollars apart.

With his alternative plan torpedoed by his own party, Boehner said it now is time for Obama and Senate Democrats to come up with a solution.

Boehner also denied a reporter's suggestion that he is walking away from further talks, but he offered no timetable or mechanism for resuming discussions.

In the Senate, Reid said all House measures on the fiscal cliff so far have failed to meet the minimum demands of Obama, such as wealthy Americans paying more to prevent an increased burden on middle-class families.