House Speaker John Boehner today sent President Obama a counter-proposal on how to cut the deficit that he called a "credible plan" to break the stalemate in negotiations to keep the country from going off the "fiscal cliff" but just hours later the White House quickly rejected the offer.

In the plan, Republicans offer a total of $2.2 trillion in deficit reduction over the next decade. That would give lawmakers "ample" savings to off-set $1.2 trillion in automatic cuts set to begin to take effect Jan. 2, 2013. Senior Republican aides said the proposal does not explicitly include an offer to address the standoff over whether the president or Congress should have power over debt limit increases.

White House communications director Dan Pfeiffer rejected the GOP's counteroffer, complaining that it "does not meet the test of balance."

"Their plan includes nothing new and provides no details on which deductions they would eliminate, which loopholes they will close or which Medicare savings they would achieve," Pfeiffer stated. "While the president is willing to compromise to get a significant, balanced deal and believes that compromise is readily available to Congress, he is not willing to compromise on the principles of fairness and balance that include asking the wealthiest to pay higher rates."

Brendan Buck, a spokesman to the speaker, said that by rejecting the offer, "the White House has once again demonstrated how unreasonable it has become" and he said "it is now [Obama's] obligation to present a plan that can pass both chambers of Congress."

The GOP deal would create $800 billion in new revenue through tax reform, but Boehner insisted that tax rates should not go up on the top 2 percent of taxpayers. Instead, the GOP wants lower tax rates after closing loopholes, limiting tax credits and capping deductions.

"We believe through tax reform that you absolutely could lower rates below what they are for this year, and still hit the $800 billion target," a senior GOP leadership aide said. "How much you would be able to lower rates depends on what else you're doing in tax reform, but it's a number that's mathematically consistent with not raising rates and doing comprehensive tax reform."

The offer also proposes $600 billion in health savings, $300 billion in additional mandatory savings, $300 billion in discretionary spending cuts, and $200 billion by updating the formula by which the Consumer Price Index is calculated, which would affect all sorts of federal programs from Social Security to federal pensions.

"What we're putting forth is a credible plan that deserves serious consideration by the White House, and I would hope that they would respond in a timely and responsible way," Boehner, R-Ohio, told reporters today when he dropped into a staff briefing on the pitch. "We could have responded in kind, but decided not to do that."

A senior Republican aide also said health care savings is a mandatory element of a comprehensive deal.

"That has been in every one of these sets of conversations that we've had over the last 15 months, and I don't think there's any way to get to a comprehensive deal that solves this situation without it," the aide said. "Means testing has been, likewise, a part of every single discussion."

Boehner said the president's offer last week was "basically the president's budget from last February," which he noted received no votes in the House and no votes in the Senate.

"Going over the cliff will hurt our economy and hurt job creation in our country. It's one of the reasons why the day after the election, I offered a concession to try to speed this process up by putting revenue on the table," Boehner said. "Unfortunately the White House responded with the La-la-land offer that couldn't pass the House, couldn't pass the Senate."

Now, in a letter to the president, House Republicans say they devised an offer based on Erskine Bowles' proposal to the Joint Select Committee on Deficit Reduction, the so-called supercommittee. But Bowles himself issued a statement that the counteroffer "does not represent" his proposal to the supercommittee, since his plan was created to demonstrate how a deal could be achieved last year as negotiations faltered.

"The Joint Select Committee failed to reach a deal, and circumstances have changed since then," Bowles said this afternoon. "It is up to negotiators to figure out where the middle ground is today. "

Last week, the president asked for about $1.6 trillion in new revenue, including about $800 billion from allowing tax cuts on income over $250,000 a year expire. Obama also asked for about $400 billion in new stimulus spending, but the plan was rejected by Republicans as a "step backward."

The letter with the GOP's proposal was sent to the president around 2 p.m. today. One senior Republican aide close to the negotiations admitted the counteroffer "is not something that a bunch of conservatives are going to be jumping up and down endorsing."

House Minority Leader Nancy Pelosi, D-Calif., said the proposal is "another assault on the middle class, seniors, and our future."

"The American people made clear that they want us to work together on a balanced approach; yet, in the Republican plan, any alleged resemblance to an offer seeking balance and fairness is nonexistent. It only makes matters worse," Pelosi said. "Republicans are simply digging in their heels by refusing to ask the wealthiest Americans to pay their fair share and actually calling for lower tax rates."

The speaker said he did not intend to speak with the president personally about the offer, but he "might run into him" tonight at a holiday reception at the White House. Pelosi is also scheduled to attend the party.

Get more pure politics at ABC News.com/Politics and a lighter take on the news at OTUSNews.com

ABC News' Mary Bruce contributed to this article