The White House and leading congressional Democrats immediately rejected Boehner's "Plan B," which would extend soon-to-expire Bush-era tax cuts for everyone making less than $1 million but would not address huge across-the-board spending cuts that are set to strike the Pentagon and domestic programs next year.
"Everyone should understand Boehner's proposal will not pass the Senate," said Senate Majority Leader Harry Reid, D-Nev.
Boehner's surprise move came after significant progress over the past several days in talks with Obama - talks that produced movement on tax rate hikes that have proven deeply unsettling to GOP conservatives and on cuts to Social Security benefits that have incensed liberal Democrats.
Just Monday, Obama offered concessions, including a plan to raise top tax rates on households earning more than $400,000 instead of the $250,000 threshold he had campaigned on. And the two sides had inched closer on the total amount of tax revenue required to seal the agreement. Obama now would settle for $1.2 trillion over the coming decade while Boehner is offering $1 trillion.
By contrast, protecting income below $1 million from a hike in the top tax rate from 35 percent to 39.6 percent would raise only $269 billion over the coming decade.
But the outlines of a possible Obama-Boehner agreement appeared to have shaky support at best from Boehner's leadership team and outright opposition from key Republicans like vice presidential nominee Paul Ryan, R-Wis., a House GOP aide said. That aide spoke only on condition of anonymity because the aide was not authorized to discuss the situation publicly.
Though Obama spokesman Jay Carney had nothing good to say about Boehner's new option, he said, "The president is willing to continue to work with Republicans" toward a broader agreement.
The narrower Plan B faced plenty of opposition. Democrats announced they would oppose it, and many conservative Republicans continued to resist any vote that might be interpreted as raising taxes. Republicans were refining the measure Tuesday in hopes of building support among the GOP rank and file, but passing the measure exclusively with GOP votes could prove difficult.
"I think it's a terrible idea," said Rep. Raul Labrador, R-Idaho. "For a lot of reasons."
Republicans noted that top Democrats like Minority Leader Nancy Pelosi of California and Sen. Charles Schumer of New York have in the recent past supported the million-dollar threshold for rates hikes. "We've had an election on the President's tax plan, the President won, and Republicans can't turn the clock back," said Schumer spokesman Brian Fallon.
Boehner's back-up plan would extend current income tax rates except for income exceeding $1 million, set a 20 percent tax rate on capital gains and dividend income for income over $1 million instead of 15 percent now, and retain current rules regarding the estate tax instead of tighter parameters sought by Obama.
It would also prevent an expansion of the alternative minimum tax that would otherwise hit 28 million middle- and upper-class Americans with an average $3,700 increase on their 2012 tax returns.
Several rank-and-file House Republicans said the message they heard at an evening caucus was that passing plan B would strengthen Boehner's hand in negotiating steeper spending cuts with Obama.
"It strengthens his hand because it shows he can get something done," said Rep. Steve Stivers, R-Ohio.
Democrats said Boehner's move made it clear he was abandoning efforts to reach an agreement with Obama - much as he quit talks with Obama 18 months ago.
"Plan B is yet another example of House Republicans walking away from negotiations," said Rep. Chris Van Hollen, D-Md., top Democrat on the Budget Committee.
At the White House, officials remained cautiously optimistic that the talks could get back on track despite Boehner's maneuvering.
Boehner, however, said Obama is the one proving to be too inflexible, even as he held out hope that talks with Obama might yet bear fruit.
"He talked about a 'balanced' approach on the campaign trail," Boehner said. "What the White House offered yesterday - $1.3 trillion in revenue for only $850 billion in spending cuts - cannot be considered balanced."
Boehner also displayed new flexibility on the politically explosive issue of raising the Medicare retirement age from 65 to 67. Boehner said the idea - anathema to Democrats - didn't need to be dealt with this year but could be kicked over into a broader negotiation next year.
"That issue has been on the table, off the table, back on the table," Boehner said. "I don't believe it's an issue that has to be dealt with between now and the end of the year."
Just Monday, the Capitol bristled with optimism that Boehner and Obama might strike a bargain.
In a new offer, Obama dropped his long-held insistence that taxes rise on individuals earning more than $200,000 and families making more than $250,000. He is now offering a new threshold of $400,000 and lowering his 10-year tax revenue goals from the $1.6 trillion he originally sought.
The new Obama plan seeks $1.2 trillion in revenue over 10 years and $1.2 trillion in 10-year spending reductions. Boehner aides say the revenue is closer to $1.3 trillion if revenue triggered by a new inflation index is counted, and they say the spending reductions are closer to $930 billion if one discounts about $290 billion in lower estimated debt interest.
The two sides also differ on the estate tax, extending unemployment benefits and how to address the need to raise the government's borrowing cap to prevent a first-ever U.S. default and a re-run of last year's debt crisis.
The White House was facing its own backlash, with labor, liberal and elderly advocacy groups mounting an organized campaign against any adjustments in cost-of-living for Social Security beneficiaries.
"President Obama and other Democrats campaigned saying Social Security doesn't affect the deficit," said Roger Hickey, co-director of the liberal Campaign for America's Future. "Social Security recipients are going to notice and they are either going to blame John Boehner or President Obama."
The change would reduce annual cost-of-living increases for beneficiaries of Social Security and other government programs. It also would push more people into higher tax brackets by making smaller annual adjustments to brackets.
The administration appeared confident that most Democrats would reluctantly vote for the idea in an attractive enough budget package, particularly one that has the backing of Obama.
"I think many of us still have faith that the president will ultimately, if he strikes a deal with the Republicans, give us a plan that we can vote on that provides that fairness and balance," said Rep. Xavier Becerra, D-Calif.
White House spokesman Carney described the inclusion of the inflation adjustment as "a technical change" that was "not directed at one particular program." He also said that if instituted, the administration would ensure that the most vulnerable beneficiaries would not be affected.
Associated Press writers Alan Fram, Jim Kuhnhenn and Donna Cassata contributed to this report.