WASHINGTON — President Barack Obama said he’ll press ahead with Congress in hopes of preventing across-the-board tax increases set to strike taxpayers Jan. 1 after House GOP leaders unexpectedly put off a vote on legislation calling for higher rates on million-dollar earners Thursday evening.

The measure “did not have sufficient support from our members to pass,” House Speaker John Boehner, R-Ohio, conceded in a brief statement.

At the White House, Press Secretary Jay Carney said that Obama’s “main priority is to ensure that taxes don’t go up on 98 percent of Americans and 97 percent of small businesses,” citing statistics associated with Obama’s campaign promise to increase top tax rates on households earning more than $250,000 a year.

“The President will work with Congress to get this done and we are hopeful that we will be able to find a bipartisan solution quickly that protects the middle class and our economy,” Carney said. Pointedly, the statement didn’t say whether Obama would work with Boehner to revive stalled talks or turn first to the Democratic-controlled Senate to try to salvage the situation.

Boehner’s attempt to tactically 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 Senate Majority Leader Harry Reid, D-Nev., made is clear that Plan B would have been dead on arrival in the Senate.

“Speaker Boehner’s plans are non-starters in the Senate,” Reid said.

Boehner announced he would move to Plan B after testing the waters with fellow Republicans regarding a possible pact with Obama on tax increases of $1 trillion — including the breakthrough proposal on higher tax rates — and finding them not very receptive.

Thursday’s 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 his written statement, Boehner said the House has previously passed legislation to prevent all the tax increases from taking effect, and noted that earlier in the evening it had approved a measure to replace across-the-board spending cuts with “responsible” reductions.

In arguing for legislation with a million-dollar threshold for higher tax rates, Boehner said the president has called for legislation to protect 98 percent of the American people from a tax hike. “Well, today we’re going to do better than that,” he said of the measure that raises total taxes by slightly more than $300 billion over a decade. “Our bill would protect 99.81 percent of the American people from an increase in taxes.”

Democrats said that by keeping tax rates unchanged below $1 million — Obama has offered a compromise $400,000 level — Republicans had turned the bill into a tax break for the wealthy. They also accused Republicans of crafting their measure to impose a tax increase on 11 million middle class families.

“This is a ploy, not a plan,” said Rep. Sander Levin, D-Mich. He accused Republicans of being “deeply cynical,” saying the legislation would scale back some education and child tax credits.

A companion bill on the evening’s House agenda, meant to build GOP support for the tax bill, 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.

Ironically, the votes were set in motion earlier in the week, after Boehner and Obama had significantly narrowed their differences on a compromise to avoid the fiscal cliff.

Republican officials said that 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 rank and file to win the votes needed for the type of agreement he was negotiating with the president.

Asked at a news conference a few hours before the scheduled vote if that were so, Boehner avoided a direct answer. “Listen, the president knows that I’ve been able to keep my word on every agreement we’ve ever made,” he said.

By any measure, the two bills in the House were far removed from the latest offers that officials said Obama and Boehner had tendered. And 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.