It can't be done. Preposterous. Lawmakers will never agree.

All are common responses to calls for the federal government to slash and burn its bloated budget, which has grown by more than $700 billion over just the last three years.

But if the debate this week over the extension of the Bush tax cuts and other benefits offers any lesson, it's that Washington will have to defy expectations and start cutting soon. In order to hold tax rates to the level lawmakers want, they'll need a budget scalpel the size of a battle axe.

House Republicans are talking about doing this, and budget analysts say a 10 or 20 percent cutback isn't just necessary -- it's possible.

"It's a big lift," said Chris Edwards, director of tax policy studies with the Cato Institute. "Some people are sort of defeatist ... but I don't think (their assumptions are) true."

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Edwards just released a proposal that would slash 20 percent from the annual budget by the end of the decade. The proposal includes GOP wish-list items like repealing the 2010 health care law that are simply not possible in the current climate, as well as Reagan-era promises like eliminating the Education Department, but it also has a bundle of ideas hardly foreign to professional budget scrutinizers.

Among them: Edwards projects $57 billion in savings from cutting or ending farm, food and other subsidies. He projects $150 billion in savings from Defense Department cutbacks including a shutdown of extraneous overseas bases -- something libertarian Rep. Ron Paul, R-Texas, has advocated. He recommends cutting foreign aid by half for a savings of $12 billion and raising $93 billion by making changes to Social Security like raising the retirement age. He calls for a hefty increase in Medicare premiums and the elimination altogether of the Department of Housing and Urban Development, as well as the privatization of Amtrak and air traffic control.

Cutting popular programs and emasculating departments that provide a vehicle for federal aid may be anathema to political instincts, but Edwards argued the overall goal needs to be getting the federal government out of areas that state and local governments can handle more effectively. He argued that housing subsidies can distort the market; ditto for farm aid. Edwards cited the case of New Zealand, where the government eliminated farm subsidies in the mid-'80s, but the industry thrived anyway. And despite the apparent staleness of the pitch to shut down the Education Department, critics frequently point to the fact that test scores have not risen significantly in spite of all that federal aid -- a point hammered in the recent documentary, "Waiting for Superman."

At the midway point through President Obama's term, and as Republicans prepare to take control of the House, spending cuts have not moved to the front burner by any means.

The Obama administration and congressional Republicans this week have been pushing an $850 billion package of tax cut extensions, unemployment aid and other benefits. The size of the package led one senator to accuse Washington of suffering from short-term amnesia, as it came just days after the president's deficit commission warned of a debt crisis on the rise. The commission issued a year-end report calling for sweeping reforms in Social Security and Medicare, and cuts all across the federal budget, to at least stabilize the national debt. That report did not make it out of the committee.

Obama, interviewed on NPR, noted that he had not "specifically endorsed" that proposal, though he backed some of its concepts. He played down proposals to cut earmarks and cut foreign aid, saying they wouldn't amount to much.

"We're not going to be able to deal with our deficit just by eliminating foreign aid," Obama said. "That only accounts for 1 percent of our budget. ... We've got to look at a whole range of things" including entitlements, defense spending and discretionary spending. "

But lawmakers are trying to start somewhere, even if it's small potatoes. House Republican Leader John Boehner, who has called for a return to fiscal 2008 levels for non-security discretionary spending, said in an interview with CBS' "60 Minutes" that one of the first votes he would call for as speaker would be to cut pay in Congress. Boehner said that would include a 5 percent cut for leadership budgets including his, a 5 percent cut for committee budgets and a 5 percent cut for members' allowances. He estimated it could save $25-30 million.

Obama, likewise, has called for a two-year freeze in civilian federal worker pay, which the administration estimates would save $5 billion during that period.

It's a start. But it wouldn't end there.

Brian Riedl, top budget analyst at the conservative Heritage Foundation, put out a recent proposal to cut about 10 percent -- or $343 billion -- from the total federal budget.

Some of the ideas might sound familiar -- reforming farm subsidies, cutting back the Department of Education and privatizing Amtrak. He also calls for eliminating community development block grants, cutting the federal employee travel budget by $10 billion, eliminating homeland security grants to states for a savings of $2.7 billion and eliminating the "duplicative" Office of National Drug Control Policy.

Riedl argued that the federal government has obligated itself to so much spending because it has expanded into education, transportation and economic development programs, among others, that are best left to the states.

"There's no reason for Washington to be running those programs," he said.

Balancing the budget, now at $3.5 trillion, and getting control of the national debt would likely require more than $343 billion. But as steep as that figure is, Riedl estimated that one would only have to look back to the 2007 budget, adjusted for inflation, to see a spending plan that was 20 percent smaller than it is now.

What would it be like to cut back even further? Paul estimated, in one of his myriad manifestos, that a 40 percent cut from the 2007 budget would send the country back to 1997 levels - not so long ago. (That estimate, though, was delivered in the course of an argument for the elimination of the income tax -- in which case the U.S. government would still have a deficit problem.)

Obama told NPR that in order to tackle the debt and deficit, it won't mean "Armageddon" and the government doesn't have to "slash and burn everything."

But trimming around the edges also won't work, analysts say.

"The alternative is we're going to have to have massive tax hikes, and I just think the public is going to reject that," Edwards said.