Updated: 12:25 p.m.

House Budget Chairman Paul Ryan said Sunday that the fiscal 2012 budget proposal he will release this week would cut more than $4 trillion over the next decade, make sweeping changes to Medicare and Medicaid, cap federal spending, and reduce tax rates.

While the Wisconsin Republican made the case that the elements of his proposal are needed to put the nation’s soaring debt on a “downward trajectory,” he acknowledged that the package, which he plans to release Tuesday, could provide fodder for Democrats in the 2012 election cycle.

“We are giving them a political weapon to go against us, but they will have to lie and demagogue to make that a political weapon,” Ryan said on “Fox News Sunday.” “They are going to demagogue us, but it’s that demagoguery that has always prevented political leaders in the past from trying to fix the problem. … Yes, we will be giving political adversaries things to use against us in the next election, and shame on them if they do that.”

Ryan said he would propose changing Medicare by replacing the current structure with a “premium support system,” sometimes referred to as a voucher system, that he said was modeled after a plan he developed last year with Alice Rivlin, who served as budget director to President Bill Clinton. The change would not affect individuals older than 55.

Ryan said his proposal would function similarly to the Medicare prescription drug benefit and would direct fewer federal dollars to wealthy seniors while protecting low-income individuals.

“The problem is, the biggest driver of our debt is Medicare,” he said.

Ryan also said he would seek to slow the rate of growth in Medicaid spending, in part by proposing block grants to states.

Ryan was short on specifics, saying that he and his staff were still fine-tuning their numbers, but that his proposed budget would cut more than $4 trillion over the next 10 years, exceeding the goal set last year by President Barack Obama’s National Commission on Fiscal Responsibility and Reform. He said the proposal would cap discretionary spending at a lower level than Obama proposed and cap all federal spending as a percentage of gross domestic product.

Ryan also said he would propose “pro-growth” changes to the tax code, including a reduction in corporate taxes, based around broadening the tax base and lowering rates. But he stressed that spending reductions were the key element in his budget proposal.

“We don’t have a tax problem,” Ryan said. “The problem with our deficit is not because Americans are taxed too little. The problem with our deficit is because Washington spends too much money. We have got to stop spending money we don’t have.”

Sen. Mark Warner, a leader of the “Gang of Six,” which is working to implement the recommendations of Obama’s fiscal commission, said Sunday that he was anxious to see the details of Ryan’s proposal.

“My understanding is he’s going to do all these things and not look at defense spending, not look at tax reform that would actually raise revenues,” the Virginia Democrat said on CNN’s “State of the Union.” “I don’t know how you get there without taking basically a meat ax to those programs who protect the most vulnerable in our country. … I think the only way you’re going to really get there is if you put all of these things, including defense spending, including tax reform, as part of the overall package.”

The Gang of Six will put forth its plan “very shortly,” Warner said, and another member, Senate Majority Whip Dick Durbin, told NBC’s “Meet the Press” to expect the bipartisan group to take a different approach.

“This group of six Senators — three Democrats and three Republicans — which I’ve been part of, we’re trying to come up with a bipartisan approach in the Senate to address the same issues that Paul Ryan addresses in his budget,” the Illinois Democrat said. “I think we’ll come at it differently. What we need to see is everything on the table and real balance. The idea of sparing the Pentagon from any savings, not imposing any new sacrifice on the wealthiest Americans, I think goes way too far. We’ve got to make certain that it’s a balanced approach and one that can be sustained over the next 10 years.”

National Republican Senatorial Committee Chairman John Cornyn, who appeared on “State of the Union” with Warner, accused Obama of failing to lead on spending reductions and charged some Democratic lawmakers, such as Senate Democratic Conference Vice Chairman Charles Schumer (N.Y.), with criticizing Republicans “for the proposals they’ve made, rather than trying to work in a constructive way.” Cornyn and Warner are both members of the Senate Budget Committee.

“The reason why Congressman Ryan is leading with this budget proposal is because the president refuses to lead, and so Republicans in the House are going to have to lead,” the Texas Republican said.