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Putting the ball back in President Obama's court, House Republicans countered Monday with what they described as a "bold" plan to avert the looming fiscal crisis -- after the White House produced a tax-heavy proposal last week that GOP leaders decried as a "joke."

Answering White House calls to present an "alternative," House Republican leaders unveiled a plan that would agree to $800 billion in "revenue through tax reform" over the next 10 years. It marks a significant step for House Republicans, some of whom opposed such increased revenue before last month's election.

However, the number is half the $1.6 trillion in tax hikes that Obama proposed and Republicans swiftly rejected. And the two sides are likely to continue to butt heads over the issue of an increase in tax rates for the top 2 percent of earners.

The White House has insisted on raising those rates next year, while Republicans favor raising revenue instead by closing deductions for top earners and other measures. They reiterated their opposition to tax-rate hikes in the plan Monday.

The White House almost immediately criticized the Republicans' offer.

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“The (proposal) does not meet the test of balance," Communications Director Dan Pfeiffer said. "In fact, it actually promises to lower rates for the wealthy and sticks the middle class with the bill. ... 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."

Fox News is told that the plan is based on that produced by the deficit-reduction commission Obama appointed - the president never embraced that plan, which got mixed reviews from Democrats and Republicans on the Hill.

In a letter to Obama on Monday, though, Republicans said they "cannot in good conscience agree" to the president's proposal, which was unveiled last week by Treasury Secretary Timothy Geithner, calling it "neither balanced nor realistic."

"Regrettably, the proposal he outlined on behalf of your administration contains very little in the way of common ground," they wrote, particularly assailing the administration's push for more stimulus spending at a time when Washington is supposed to be trimming the deficit.

The Republican counter-offer includes $800 billion in revenue through tax reform; $600 billion in health savings; $300 billion in other entitlement savings; and another $300 billion in savings elsewhere in the discretionary federal budget. The plan would hike the Medicare eligibility age and lower cost-of-living adjustments for Social Security.

Republicans estimate the plan would save $2.2 trillion over 10 years -- or $4.6 trillion if one uses the accounting methods employed by the White House. Those methods boosted the White House estimate for its own plan to $4 trillion, but Republicans say the methods are spurious.

In the letter signed by House Speaker John Boehner and other Republican leaders, the lawmakers called the plan an "imperfect, but fair middle ground."

"If you are agreeable to this framework, we are ready and eager to begin discussions about how to structure these reforms so that the American people can be confident that these targets will be reached," they wrote.

Republicans were fuming last week over the president's call for $1.6 trillion in tax hikes -- four times the value of his proposed spending cuts. Boehner said he was "flabbergasted" by the plan.

The administration's latest proposal includes roughly $600 billion in spending cuts. Those cuts, however, would be offset by $200 billion in proposed stimulus and other spending programs. The multi-year stimulus program would include at least $50 billion in fiscal 2013 alone; the administration also wants an extension of unemployment aid. And, in what one House Republican source called a "pipe dream," the administration called for effectively implementing a permanent increase in the debt limit.

The latest Republican proposal was silent on the issue of the debt ceiling.

But Republicans continued to voice opposition to raising rates. On a Twitter Q&A hosted by the White House, House Speaker John Boehner tweeted, "How does raising tax rates on ~1M #smallbiz create jobs & grow economy?"

House Majority Leader Eric Cantor also tweeted, "Let's protect small businesses and families from a harmful increase in tax rates and cut spending."

Obama, though, defended his plan on the Twitter chat.

"High end tax cuts do least for economic growth & cost almost $1T. extending middle class cuts boosts consumer demand & growth," he wrote.

White House Press Secretary Jay Carney also claimed Americans "overwhelmingly disagree" with Republicans on that point.

"Rates have to rise, and the Republicans need to acknowledge that," Carney said.

Should the White House and Congress fail to reach a deal, a $500 billion mix of tax hikes and austere cutbacks on federal spending will kick in Jan. 1.

Late Monday, Senate Majority Leader Harry Reid also criticized the plan.

“To protect millionaires, Speaker Boehner’s offer would force middle-class families to pay higher taxe," the Nevada senator said. “Democrats are willing to compromise, but any agreement must protect the middle class."

Fox News' Chad Pergram contributed to this report.