WASHINGTON (AP) — House Speaker John Boehner signaled on Friday he's still open to negotiations with President Barack Obama on avoiding across-the-board tax increases set to hit taxpayers Jan. 1, but sounded pessimistic about reaching a grand deal with the president.

"How we get there, God only knows," Boehner told a Capitol Hill news conference just hours after his rank-and-file handed him a stunning tactical defeat.

The Republican leader spoke the morning after he was forced by his members to abandon legislation that would have raised taxes on incomes above $1 million.

In the aftermath, Boehner said any deal with the president to avoid the looming "fiscal cliff" would require more compromise by Obama and greater involvement of Senate Majority Leader Harry Reid, D-Nev., and the minority leader, Mitch McConnell, R-Ky.

But compromise appeared elusive in the Senate, where Reid and McConnell swapped barbs over how to deal with tax rates.

Reid again called on the House to pass an Obama-backed Senate plan to raise top tax rates on households making more than $250,000 a year. He also urged Boehner to return to the negotiating table with Obama.

McConnell countered with an offer to vote on prior House legislation extending all Bush-era tax rates — including those earning more than $1 million — a measure that's more generous to upper-bracket taxpayers than even the failed House measure. He appeared to suggest he would delay any attempt to pass Obama's plan.

McConnell said that if Democrats have a plan that can win a filibuster-proof 60 votes in the Senate then "let's vote."

Boehner dismissed suggestions that the embarrassment late Thursday night over the legislation would cost him his speakership, second in line to the presidency. In a show of support, Majority Leader Eric Cantor, R-Va., stood by Boehner's side.

"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. "They were dealing with the perception that somebody might accuse them of raising taxes."

Obama has said he will press ahead with Congress in search of a deal and that the two sides are relatively close to a long-sought budget bargain. But Boehner on Friday depicted an impasse.

"I told the president on Monday these were my bottom lines," Boehner said. "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." Boehner and the White House differ on how to classify key elements of Obama's latest offer, particularly whether to count interest savings on the national debt as a spending cut. The White House says Obama offered $1.2 trillion in spending cuts, matched by $1.2 trillion in higher taxes.

White House Press Secretary Jay Carney 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, because after all, unlike his counterparts in this negotiation, he has already gone halfway on both sides of the equation."

Boehner's attempt to retreat from a longstanding promise to maintain Bush-era tax rates for all was designed to gain at least some leverage against Obama and Senate Democrats in the fiscal cliff endgame. Thursday's drama was a major personal defeat for the speaker, who retains the respect and affection of his tea party-infused conference, but sometimes has great difficulty getting them to follow his leadership.

What Boehner called his "Plan B" was crafted to prevent tax increases set to kick in Jan. 1 on virtually every taxpayer. But it also would have provisions that would have let rates rise for those at the upper income range — a violation of long-standing Republican orthodoxy that triggered opposition inside the party.

The hope was that successful House action on the measure would force Senate Democrats to respond. But Reid made clear that Plan B would have been dead on arrival in the Senate.

The latest events leave little time for Obama and bruised lawmakers to prevent across-the-board tax increases and deep spending cuts from taking effect with the new year. Economists say the combination threatens a return to recession for an economy that has been recovering slowly from the last one.

The House will not meet again until after Christmas, if then, and the Senate is expected to meet briefly on Friday, then not reconvene until next Thursday.

In arguing for legislation with a million-dollar threshold for higher tax rates, Boehner said the president has called for protecting 98 percent of people from a tax increase. His bill would "protect 99.81 percent of the American people from an increase in taxes."

A companion bill that was meant to build GOP support for the tax legislation called for elimination of an estimated $97 billion in cuts to the Pentagon and certain domestic programs over a decade. It cleared the House on a partisan vote of 215-209 and is an updated version of legislation that passed a little more than six months ago.

Those cuts would be replaced with savings totaling $314 billion, achieved through increases in the amount federal employees contribute toward their pensions and through cuts in social programs such as food stamps and the health care law that Obama signed earlier in his term.

Earlier in the week, Boehner and Obama had significantly narrowed their differences on a compromise to avoid the fiscal cliff.

But Republican officials said members of the GOP leadership had balked at the terms that were emerging. Democrats said Boehner's abrupt decision to shift to his Plan B — legislation drafted unilaterally by Republicans — reflected a calculation that he lacked support from his own members to win the votes needed for the type of agreement he was negotiating with the president.

By any measure, the two bills in the House were far removed from the latest offers that officials said Obama and Boehner had tendered. The two men don't seem to be that far apart.

Obama is now seeking $1.2 trillion in higher tax revenue, down from the $1.6 trillion he initially sought. He also has softened his demand for higher tax rates on household incomes so they would apply to incomes over $400,000 instead of the $250,000 he cited during his successful campaign for a new term.

He also has offered more than $800 billion in spending cuts over a decade, half of it from Medicare and Medicaid, $200 billion from farm and other benefit programs, $100 billion from defense and $100 billion from a broad swath of government accounts ranging from parks to transportation to education. In a key concession to Republicans, the president also has agreed to slow the rise in cost-of-living increases in Social Security and other benefit programs, at a savings estimated at about $130 billion over a decade.

By contrast, Boehner's most recent offer allowed for about $940 billion in higher taxes over a decade, with higher rates for annual incomes over $1 million.