Bowles, in a statement, said he was flattered but the GOP plan does not represent his proposal.
Still, he added, "Every offer put forward brings us closer to a deal, but to reach an agreement, it will be necessary for both sides to move beyond their opening positions."
By GOP math, their plan would produce $2.2 trillion in budget savings over the coming decade: $800 billion in higher taxes, $600 billion in savings from costly health-care programs like Medicare, $300 billion from other proposals, such as forcing federal workers to contribute more toward their pensions and $300 billion in additional savings from the Pentagon budget and domestic programs funded by Congress each year.
Boehner signaled in discussions with Obama in 2011 that he was willing to accept up to $800 billion in higher tax revenues, but his aides maintained that much of that money would have come from so-called dynamic scoring -- a conservative approach in which economic growth would have accounted for much of the revenue. Now, Boehner is willing to accept the estimates of official scorekeepers like the Congressional Budget Office, whose models reject dynamic scoring.
Under the administration's math, GOP aides said, the plan represents $4.6 trillion in 10-year savings. That estimate accounts for earlier cuts enacted during last year's showdown over lifting the government's borrowing cap and also factors in war savings and lower interest payments on the $16.4 trillion national debt.
Last week, the White House delivered to Capitol Hill its opening proposal: $1.6 trillion in higher taxes over a decade, a possible extension of the temporary Social Security payroll tax cut and heightened presidential power to raise the national debt limit.
In exchange, the president would back $600 billion in spending cuts, including $350 billion from Medicare and other health programs. But he also wants $200 billion in new spending for jobless benefits, public works projects and aid for struggling homeowners. His proposal for raising the ceiling on government borrowing would make it virtually impossible for Congress to block him going forward.
Republicans said they responded in closed-door meetings with laughter and disbelief.
The GOP plan is certain to whip up opposition from Democrats opposed to any action now on Social Security, whose defenders say should not be part of any fiscal cliff deal. And Democrats also are deeply skeptical of raising the Medicare age.
Both ideas were part of negotiations between Boehner and Obama in the summer of last year.
In a letter to the president, Boehner and six other House Republicans insisted that the November election that returned Obama to the White House and the GOP to majority control in the House requires both parties to come together "on a fair middle ground."
"With the fiscal cliff nearing, our priority remains finding a reasonable solution that can pass both the House and Senate, and be signed into law in the next couple of weeks," Republicans wrote.
One of the few things the White House and Capitol Hill Republicans can agree to is a framework that would make a "down payment" on the deficit and extend all or most of the expiring Bush-era tax cuts but leave most of the legislative grunt work until next year.
Signing the letter was Boehner, House Majority Leader Eric Cantor, Majority Whip Kevin McCarthy and Rep. Paul Ryan, the chairman of the House Budget Committee and the unsuccessful GOP vice presidential candidate. Rep. Dave Camp, chairman of the Ways and Means Committee, Fred Upton, chairman of the Energy and Commerce Committee, and Cathy McMorris Rodgers, the Republican Conference chair, also signed the letter.
Earlier Monday, Obama answered questions on Twitter for an hour as the White House sought to keep up the pressure on the issue.
In response to a question about his insistence on higher tax rates for the wealthiest earners, Obama said that "high end tax cuts do [the] least for economic growth & cost almost $1T." By contrast, he said, "extending middle class cuts boosts consumer demand & growth."Obama said he was open to "smart cuts" in spending, "but not in areas like R&D" and education, which "help growth & jobs." He also said he opposes spending cuts that would hurt the disabled or other vulnerable groups.