WASHINGTON (Reuters) - Republicans proposed steep spending cuts on Monday but gave no ground on President Barack Obama's call to raise taxes on the wealthiest in their first formal proposal to avert a "fiscal cliff" that could push the U.S. economy into recession.

After days of stalemate, the Republican offer shows deep differences with President Barack Obama as the two sides work to head off across-the-board spending cuts and tax increases due to take effect in January.

The White House dismissed the proposal and said it contained no new ideas. But it could allow negotiators to begin work in earnest as both sides now have outlined their visions in concrete terms. Analysts say the talks will have to show progress this week to ensure that a deal can be signed into law before the end of the year.

"The American people expect their leaders to find fair middle ground to address the nation's most pressing challenges," House of Representatives Speaker John Boehner of Ohio and several other top House Republicans wrote in a letter to Obama.

Both the Republican and White House plans would rely on spending cuts and increased tax revenue to trim budget deficits by more than $4 trillion over the coming 10 years. According to the Republicans, their plan would save $240 billion more than Obama's proposal.

Beyond the headline numbers, the two plans reveal deep philosophical divisions about how the country should balance tax increases and spending cuts to put the country's finances on a sustainable course.

Republicans envision $1 trillion more in spending cuts than Obama has proposed, while Obama wants $800 billion more in tax increases and $200 billion in measures to boost the sluggish economy.

The Republican proposal would overhaul the complicated U.S. tax code to raise $800 billion in new revenue. Boehner tentatively agreed to that much in new tax revenue, presumably from closing loopholes in deductions, in failed talks with Obama in the summer of 2011.

Monday's proposal marks the first time his party has floated a budget plan that departs from the anti-tax stance that has defined the party for decades.

But the Republicans said they would oppose raising tax rates on the wealthiest 2 percent of U.S. households, which is a central element of Obama's proposal.

"Until the Republicans in Congress are willing to get serious about asking the wealthiest to pay slightly higher tax rates, we won't be able to achieve a significant, balanced approach to reduce our deficit," White House communications director Dan Pfeiffer said in a prepared statement.

The Republican plan would also trim government healthcare costs by $600 billion over a decade, $250 billion more than Obama proposed in his opening bid last week.

It would slow the growth of cost-of-living increases on federal benefits by $200 billion by changing the way they are calculated and cut other government spending by $600 billion.

MUTUAL DISTRUST

The cuts proposed by Republicans are sure to face fierce resistance from Democrats, who are still smarting over $1.1 trillion in cuts that Republicans extracted in a budget deal last year.

The top Democrats in the House and the Senate said the plan was unacceptable because it would hurt the middle class while protecting the wealthy. House Democratic Leader Nancy Pelosi said she would try to force a vote on Tuesday to raise tax rates for the wealthiest.

Negotiators must overcome more than just mutual distrust as they work toward a deal in coming weeks. While some business leaders and grassroots groups are urging Washington to craft a "grand bargain" that would put federal finances on a sustainable course, lawmakers also face a more immediate lobbying blitz from groups that worry that any deal could decimate favored federal programs.

Anti-tax activist Grover Norquist has been in the spotlight as he pressures Republicans to stick by a pledge many have signed to oppose any tax increases.

On the other side of the ledger, industry groups are scrambling to protect spending on everything from education to defense and scientific research. Liberal groups have mobilized to protect popular federal health and retirement programs.

"Everyone wants something to happen before the end of the year, but what's more important than having something happen is having the right thing happen," said Nancy Altman, co-director of Social Security Works, a coalition of liberal and labor groups.

"A bad deal is worse than no deal at all," she said.

Several defense contractors said their business has already been hurt by concerns about the looming, across-the-board spending cuts that will take effect in January absent a deal.

"We are talking a good game, but are still unwilling to park short-term self-interest," said David Langstaff, chief executive of engineering firm TASC Inc. "Every trade group, special interest and corporate lobbyist is up on Capitol Hill clamoring that Congress solve the problem ... but don't touch my budgets! We can't have it both ways."