Washington (CNN) -- House Budget Chairman Paul Ryan said Sunday he will unveil a Republican budget for 2012 this week that proposes dramatic changes to Medicare, Medicaid and other political lightning rods.

The plan, to be released Tuesday, calls for a controversial overhaul of Medicare, the health care program for seniors, and would impose deep cuts in Medicaid, which provides health benefits to low-income Americans, Ryan told "Fox News Sunday."

Starting 10 years from now, in 2021, elderly Americans would receive government help in paying health insurance premiums instead of enrolling in the government-run Medicare program, Ryan said. He rejected the label of "vouchers" for the payments, calling them "premium assistance" payments instead.

The plan is modeled after one Ryan proposed last year with Alice Rivlin, budget director under President Bill Clinton. The Ryan-Rivlin plan said the amount of assistance would be calculated in part by taking the average federal cost per Medicare enrollee.

In its analysis of the Ryan-Rivlin plan, the non-partisan Congressional Budget Office said it involved vouchers. Republican sources have admitted to CNN that the term "vouchers" is politically explosive, especially for such a controversial set of changes like those being proposed by Ryan.

His proposal would only affect people younger than 55, with those 55 and older continuing to receive Medicare benefits under the existing system, Ryan said.

The proposal was intended to provide help to low-income senior citizens while requiring wealthier senior citizens to pay more for their health coverage, he said.

On Medicaid, Ryan's proposal would provide states with block grants to cover the costs of health coverage for the poor. Sources said the plan would cut Medicaid spending by up to $1 trillion, though Ryan provided no specific figure on Sunday.

Medicare and Medicaid are part of federal entitlement programs that comprise the lion's share of federal spending. So far, negotiations on federal spending for the rest of the current year -- fiscal 2011, which ends on September 30 -- have focused solely on cuts in non-security discretionary spending, with no changes in Medicare, Medicaid or Social Security.

Ryan, R-Wisconsin, said his plan would bring "well over" $2 trillion in savings in coming years, and he criticized President Barack Obama for offering a 2012 budget proposal that contained no reforms of entitlement programs.

In addition, Ryan said, his proposal would change the tax code to lower rates but eliminate some exemptions and broaden the tax base. Asked for specifics, he instead repeated the Republican mantra that the nation needed to cut spending to balance the budget and reduce deficits, not raise taxes.

Democratic Sen. Mark Warner of Virginia raised questions about Ryan's plan on CNN's "State of the Union."

"My understanding is he will do all of these things and not look at defense spending, not look at major tax reform that would raise revenues," Warner said, later adding: "I'll give anybody the benefit of the doubt until I get a chance to look at the details, but I think the only way you're really going to get there is you have to put everything there, including defense spending and tax reform as part of the overall package."

Sources told CNN that the House GOP budget plan does not call for significant change to the Social Security program. Republicans argue that while Social Security is a factor in the nation's fiscal crisis, it doesn't contribute as much to the soaring debt as Medicare.

However, two House GOP lawmakers briefed on the proposal told CNN they and others on the House Budget Committee believe it's a mistake not to tackle Social Security.

As for discretionary spending, one of the sources -- who would not speak on the record before the plan is publicly announced -- said Ryan's proposal promises to roll back spending to 2006 levels. It's unclear how much that would slash, but it is expected to be far more than the roughly $61 billion in spending cuts House Republicans passed in February.

Ryan told Fox that his plan would make discretionary spending a lower percentage of the nation's economic output. He declined to offer a specific figure for the desired percentage level, but said the plan would include caps on spending that would trigger across-the-board cuts if Congress exceeded them.

A GOP source said even with the major cuts and changes in Ryan's proposal, it would not bring the budget into balance for many years.

Still, GOP sources briefed on the plan said it would save hundreds of billions of dollars more than Obama's proposed 2012 budget, and trillions over the next 10 years.

Ryan's plan also provides for a permanent extension of all the Bush-era tax cuts that were extended last year through 2012 under a compromise with Obama. The president and most Democrats want to eliminate the lower tax rates of the Bush cuts for wealthy Americans.

House Republican leaders have been signaling for some time that they plan dramatic and controversial changes to entitlement programs in order to rein in the budget deficit and debt.

Knowing that the proposed changes will be politically risky and elicit an onslaught of criticism, Ryan, along with Republican Whip Kevin McCarthy, has been holding sessions two or three times a week with House Republicans to try to arm them with facts and figures about the gravity of the debt problem and why it needs to be fixed.

CNN was allowed into one of these meetings last month, and heard Ryan lay out for his GOP colleagues in stark terms what he calls the "tidal wave" of debt the country is facing.

"The Congressional Budget Office has this economic model where they measure the economy going forward, and they are telling us that the entire economy crashes in the year 2037 because their computer simulation can't conceive of any way in which the U.S. economy can continue," Ryan told the GOP group.

"By the time my kids are my age, just those three programs -- Social Security, Medicaid and Medicare --will consume all federal revenues. There will be no room for anything else in the federal budget," Ryan said.

When Ryan proposed a version of his Medicare overhaul idea last year, known as his "road map," Democrats skewered it and tried to use it as a campaign weapon against Republicans across the country. Republicans bolstered by support from the conservative Tea Party movement made big gains in November, winning control of the House and decreasing the majority of Senate Democrats.

Obama has often said it is important for Washington to address entitlement spending. But the president has not offered any specific proposals and Republicans suggest he is unwilling to back this rhetorical call with specifics because he wants them -- the Republicans -- to take the first risky steps.

Multiple GOP sources admit the timing of Ryan's 2012 budget proposal is tricky. It will be released in the middle of down-to-the-wire, contentious negotiations with Democrats about spending for the rest of fiscal 2011.

CNN is told GOP leaders considered delaying the release of Ryan's budget until this year's spending differences are resolved.

However, they decided to go ahead with it because they hope showing major cuts and reforms planned for next year will help calm rank-and-file conservatives who are unhappy their leadership is compromising too much on spending cuts now.

CNN's Dana Bash and Deirdre Walsh contributed to this story.