WASHINGTON — With Congress in gridlock and stocks taking a fall, President Barack Obama issued a stern summons to lawmakers Friday to pass legislation to prevent year-end fiscal cliff tax increases on millions and avoid an imminent expiration of benefits for the long-term unemployed.

Republican House Speaker John Boehner said Obama himself must give more ground to reach an agreement. He added, “How we get there, God only knows.”

Congress was shutting down, and Obama was headed to Hawaii to join his family for the holidays. But both men indicated they’d be back working to beat the fast-approaching Jan. 1 deadline with an agreement between Christmas and New Year’s.

One day after House anti-tax rebels torpedoed Boehner’s ‘Plan B’ legislation because it would raise rates on million-dollar-earners, Obama said he still wants a bill that requires the well-to-do to pay more.  “Everybody’s got to give a little bit in a sensible way” to prevent the economy from pitching over a recession-threatening fiscal cliff, he said.

He spoke after talking by phone with Boehner — architect of the failed House bill — and meeting with Senate Majority Leader Harry Reid.

Boehner’s office quickly issued a statement saying the Ohio Republican intends to return to the Capitol after Christmas “ready to find a solution that can pass both houses of Congress.” At the same time, spokesman Brendan Buck said, “we remain hopeful he (Obama) is finally ready to get serious about averting the fiscal cliff.”

At the White House, Obama projected optimism as he struggled to deal with the wreckage of weeks of failed negotiations and political maneuvering. “So call me a hopeless optimist, but I actually still think we can get it done,” he said of an elusive deal.

The president spoke at the end of a day in which stocks tumbled and congressional leaders squabbled as the fiscal cliff drew implacably closer.

Boehner spoke in the morning, describing the increasingly tangled attempts to beat the Jan. 1 deadline and head off the perilous combination of across-the-board tax hikes and deep spending cuts.

Obama spoke shortly before a scheduled departure to join his family in Hawaii for Christmas, but in an indication of the importance of the issue, he told reporters he would be returning to the White House next week.

He said that in his negotiations with Boehner, he had offered to meet Republicans halfway when it came to taxes, and “more than halfway” toward their target for spending cuts.

He said he remains committed to working toward a goal of longer-term deficit reduction, but in the meantime he said quick action is needed to keep taxes from rising for tens of millions.

“Averting this middle class tax hike is not a Democratic responsibility or a Republican responsibility. With their votes, the American people have decided that government is a shared responsibility,” he said, referring to a Congress where power is divided between the two parties.

“We move forward together or we don’t move forward at all,” he added.

Progress was invisible one day after House Republican rebels thwarted Boehner’s plan to prevent tax increases for all but the nation’s million-dollar earners. And while neither House is expected to meet again until after Christmas, officials in both parties said there was still time to prevent the changes from kicking in with the new year.

Yet they pointedly disagreed which side needed to make the first move.

“It’s time for the speaker and all Republicans to return to the negotiating table,” said Senate Democratic leader Reid.

He said that, for now, Boehner should allow a vote on legislation that would block all tax increases except for individuals making more than $200,000 and couples making $250,000 — the position that Obama carried through his successful campaign for re-election.

Reid said it would pass the House with votes from lawmakers from both parties, and, separately, some Democrats said it was possible similar legislation may yet be launched in the Senate.

Moments later, Senate Republican leader Mitch McConnell said Democrats had “spent all day yesterday defeating” the legislation in the House — even though Boehner himself said it had been deep-sixed by GOP opposition.

Countering Reid’s offer, McConnell said the Senate should pass legislation extending tax cuts at all income levels and requiring a comprehensive overhaul of the tax code. Beyond that, he said, “”Look: It’s the president’s job to find a solution that can pass Congress. He’s the only one who can do it.”

Rhetoric aside, the Dow Jones Industrial Average declined 121 points in what analysts said was a reaction to the events in the capital.

The developments marked yet another baffling turn in a week that began with news that Obama and Boehner had significantly narrowed their differences on a plan to erase the cliff. Both were offering a cut in taxes for most Americans, an increase for a relative few and cuts of roughly $1 trillion in spending over a year. Also included was a provision to scale back future cost-of-living increases for Social Security recipients — a concession on the president’s part as much as agreeing to higher tax rates was for the House speaker.

GOP officials said some senior Republicans balked at the emerging terms.

Boehner stepped back and announced what he called Plan B, legislation to let tax rates rise on incomes of $1 million or more while preventing increases for all other taxpayers.

Despite statements of confidence, he and his lieutenants decided late Thursday they were not going to be able to secure the votes needed to pass the measure in the face of opposition from conservatives unwilling to violate decades-old party orthodoxy never to raise tax rates.

Officials said as many as two dozen rank-and-file Republicans had made it clear they would oppose the bill, more than enough to send it to defeat given unanimous Democratic opposition.

At his Friday morning news conference several hours later, Boehner dismissed suggestions that he was concerned the turn of events could cost him his speakership.

“No, I am not,” he said.

“While we may have not been able to get the votes last night to avert 99.81 percent of the tax increases, I don’t think — they weren’t taking that out on me,” Boehner said of the Republican rank and file. “They were dealing with the perception that somebody might accuse them of raising taxes.”

Boehner also said that last Monday he had told Obama he had submitted his bottom line proposal.

“The president told me that his numbers — the $1.3 trillion in new revenues, $850 billion in spending cuts  —  was his bottom line, that he couldn’t go any further.”

That contradicted remarks by White House Press Secretary Jay Carney, who said on Thursday that Obama has “never said either in private or in public that this was his final offer. He understands that to reach a deal it would require some further negotiation. There is not much further he could go.”