President Obama this week will lay out a new approach to reducing the nation’s soaring debt, proposing reductions in spending on entitlements such as Medicare and Medicaid and renewing his call for tax increases on the rich.

In an effort to go on the offensive in the battle over government spending, Obama will look for cuts in “all corners of government,” senior adviser David Plouffe said on several Sunday talk shows.

Although Obama’s health-care law is projected to curtail Medicare spending over time, “we have to do more,” Plouffe said Sunday, marking the first time the administration has made an explicit commitment to changes in entitlement programs for the purpose of deficit reduction.

Contrasting the president’s approach with what Republican leaders have put forward, Plouffe said Obama will use a “scalpel” and not a “machete” as he seeks to preserve funding for education and other areas he considers crucial to the country’s long-term economic success.

Still, Plouffe said Obama is committed to doing more to slash the fast-rising cost of Medicare and Medicaid, to roll back George W. Bush-era tax cuts for those earning more than $250,000 and to even discuss changes to Social Security.

For Obama, the political stakes are high. He will be trying to convince voters concerned about the growing debt that he is serious about cutting government spending and Democratic allies that he will protect key government programs, while also working to ensure spending is not cut so much that it impairs economic recovery.

In a speech scheduled for Wednesday, Obama will present his most extensive response to date in the debate over controlling federal spending. White House advisers have been discussing for months whether he should take the lead on deficit and debt reduction, concluding that his best approach for beating back Republican proposals for much deeper cuts would be to put forward his own vision.

The new approach is coming as the president seeks a way to defuse a potentially damaging battle over how much the federal government can borrow. The debt limit is set to be reached in mid-May, and the government will be able to meet all of its obligations only through early July at the latest. Many Republicans have said they will not vote to increase the limit without significant cuts in spending.

The question hanging over Obama’s speech is whether it will contain specific new ideas for reducing spending, be a broad but not detailed endorsement of deficit reduction or just offer principles for working with Congress. Simply by putting Medicare and Medicaid on the negotiating table, the president appears to be taking a more comprehensive approach to deficit reduction than he has before.

White House and Treasury Department officials have been working on a potential overhaul of corporate tax policy, but it is unclear whether that will be part of a deficit reduction plan.

Although Obama has long acknowledged the importance of deficit reduction — there was a fiscal summit at the White House in the first months after he took office, and he appointed a fiscal commission to address the issue last year — he has not embraced the most ambitious plans to roll back borrowing.

The president did not support the full report of his fiscal commission, which offered a plan in December to cut borrowing by nearly $4 trillion by 2020. Nor did he offer significant deficit reduction in the budget blueprint he released in February. That document contained a five-year freeze on domestic discretionary spending and proposed a slew of tax increases originally offered in his previous budgets, but it also proposed nearly doubling the debt over the next 10 years.

House Republicans upped the pressure on the president last week when they introduced a plan to slash government spending by $6 trillion more than the president’s plan over the next decade — largely by shrinking Medicare and Medicaid. The House may vote this week on a resolution supporting the budget — perhaps Wednesday, the day of the president’s speech.

On Sunday, Plouffe did not specify how much more the president wants to cut or whether his speech would propose a specific legislative agenda other than to say he will be looking for savings in both Medicare and Medicaid.

He said that though Obama does not think Social Security liabilities are a primary driver of the nation’s deficit and debt, the president would be open to discussing that, too.

Republicans responded to Obama’s plan to address deficit reduction with a mixture of skepticism and openness.

House Majority Leader Eric Cantor (R-Va.) said on “Fox News Sunday” that “we had to bring this president kicking and screaming to the table to cut spending” in last week’s 2011 budget negotiations. “It’s really hard to believe what this White House and the president is saying.”

But Rep. Paul Ryan (R-Wis.), the architect of the House Republican plan to cut government spending, said that if the president “does choose to follow with serious proposals that address the drivers of our debt and the anchors holding back our economy, the door is open.”

Plouffe held open the possibility of compromise, saying that “the parties are going to have to come together to find common ground” and that the Republicans “should be credited” for advancing a plan with specific ideas to trim the deficit and debt. But, he warned, the plan was a boon for millionaires and had draconian cuts that would never be acceptable.

Obama’s decision to claim the mantle of deficit reduction comes after a White House debate on the political wisdom of doing so. White House aides have wanted to send the message to voters that Obama takes deficit reduction seriously and at the same time wants to protect programs supporting education and health care.

Some of the president’s advisers have been concerned that advancing a deficit-reduction plan would inject Obama into an unwinnable congressional fray and that his ideas would be immediately shot down.

Just in February, Obama said it was not his place to offer a plan.

“If you look at the history of how these deals get done, typically it’s not because there’s an Obama plan out there,” Obama said after releasing his 2012 budget. “It’s because Democrats and Republicans are both committed to tackling this issue in a serious way.”

Other advisers have argued that it is important that the president engage deficit reduction more publicly — at least by using the bully pulpit, if not promoting a specific plan. This would make it easier, they argued, not only to inoculate the president against criticism that he is not serious about the deficit and debt but also to protect his priorities.

In recent days, administration officials have expressed interest in the work of a bipartisan group of senators, known as the Gang of Six, who are meeting to develop a strategy for implementing the fiscal commission’s recommendations.

People familiar with those meetings said National Economic Council Director Gene B. Sperling spoke with members of the group last week to discuss the deliberations. The group is close to an agreement and may announce one as soon as next week.

“The White House is eager to attach themselves to this,” one source said.

Staff writers Lori Montgomery and Perry Bacon Jr. contributed to this report.