The proposal from House Speaker John Boehner, R-Ohio, and other Republicans comes in response to Obama's offer last week to hike taxes by $1.6 trillion over the coming decade but largely exempt Medicare and Social Security from budget cuts.
The GOP plan also proposes to raise $800 billion in higher tax revenue over the decade but it would keep the Bush-era tax cuts - including those for wealthier earners targeted by Obama - in place for now.
Boehner said the GOP proposal is a "credible plan" for Obama and that he hopes the administration would "respond in a timely and responsible way." The offer comes after the administration urged Republicans to detail their proposal to cut popular benefits programs like Medicare, Social Security and Medicaid.
"After the election I offered to speed this up by putting revenue on the table and unfortunately the White House responded with their la-la land offer that couldn't pass the House, couldn't pass the Senate and it was basically the president's budget from last February," Boehner told reporters.
The Boehner proposal revives a host of ideas from failed talks with Obama in the summer of 2011. Then, Obama was willing to discuss politically controversial ideas like raising the eligibility age for Medicare, implementing a new inflation adjustment for Social Security cost-of-living adjustments and requiring wealthier Medicare recipients to pay more for their benefits.
On Monday, Obama did not respond to questions from reporters on his reaction to the Republican counteroffer or whether he had seen the proposal. He was asked about the offer during an event in the Oval Office with the Bulgarian prime minister.
The clock is ticking closer to the end-of-year deadline to avert the fiscal cliff, which is a combination of the expiration of Bush-era tax cuts and automatic, across-the-board spending cuts that are the result of prior failures of Congress and Obama to make a budget deal.
Many economists say such a one-two punch could send the fragile economy back into recession.
GOP aides said the plan was based on a plan floated by Erskine Bowles in testimony to the special deficit "supercommittee" last year - in effect a milder version of the highly controversial 2010 Bowles proposal that caused both GOP and Democratic leaders in Congress to recoil.
By GOP math, the plan would produce $2.2 trillion in saving 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 like 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.
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 all or most of the extend expiring Bush-era tax cuts but leave most of the legislative grunt work until next year.
Republicans dismissed the notion of raising tax rates and said flatly they would oppose them. Instead, new revenue would come from tax reform, closing loopholes and deductions while lowering rates, according to the Bowles plan.
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.
In a scathing attack, Republican leader Mitch McConnell said, "if the president is serious about joining us in an effort to reduce the deficit and protect the economy, he'll get off the campaign trail, drop the left-wing talking points, and instruct his staff to negotiate a solution in good faith based on actual written proposals. In short, he'll begin doing what leaders do: Lead."