Rep. Rick Nolan (D-Minn.) speaks to a group of protesters outside the White House on Apr. 9. Liberal lawmakers from both chambers of Congress and a coalition of like-minded groups rallied in Washington, D.C., voicing frustration at President Obama for proposing cuts to Medicare and Social Security. (J. David Ake/AP)

President Obama’s offer to trim Social Security benefits has perplexed and angered Democrats, but GOP leaders are embracing the proposal and rushing to jump-start a debate that will delve even more deeply into the touchy topic of federal spending on the elderly.

This week, two House subcommittees plan to hold hearings on “reforms to protect and preserve” programs for retirees, starting with Obama’s proposal to apply a less generous measure of inflation to annual increases in Social Security benefits.

Also on the table are higher Medicare premiums and reduced benefits for better-off seniors, and a higher Medicare eligibility age.

At the same time, House Speaker John A. Boehner (R-Ohio) said he has moved to tamp down criticism of Obama’s proposal, which quickly bubbled up from GOP lawmakers in swing districts, such as Rep. Chris Collins (N.Y.), who accused the president of cutting spending “on the backs of our seniors.” And Rep. Greg Walden (Ore.), the chairman of the House Republican campaign arm, called Obama’s plan “a shocking attack on seniors.”

The developments signal an important shift in the budget battle as party leaders nervously prepare again to raise the federal debt limit. After more than two years of talking about taxes and “wasteful” government spending, policymakers appear ready to move into the more serious and sensitive realm of entitlement programs.

Republican leaders have made reducing the cost of entitlements their top priority, and for good reason, budget analysts say. Medicare, Medicaid and Social Security account for nearly 40 percent of federal spending and are growing rapidly, as they must provide benefits to all who qualify, regardless of cost.

Recipients pay into the programs throughout their working lives, and through premiums. But as the baby-boom generation retires, the programs threaten to swamp the federal budget. But relatively minor changes could make a huge difference. For example, the new inflation measure — known as the chained consumer price index, or chained CPI — would reduce benefits by only about 0.3 percentage points per year. But over the long run, it would save enough to wipe out as much as 20 percent of the program’s 75-year funding gap.

The elderly are disproportionately likely to vote, however, and although Republicans have offered a plan to overhaul Medicare a decade from now, both parties have shied away from more immediate changes, particularly to Social Security. Chained CPI has come up in private negotiations and recommendations from independent groups, such as the Bowles-Simpson commission. But Obama’s decision to include it in his formal budget request — and House leaders’ decision to hold hearings with the hope of drafting bipartisan legislation — is plowing new ground.

Still, reining in entitlement spending remains “one of the harder and stickier aspects of fiscal reform” for both parties, said Maya MacGuineas, president of the bipartisan Committee for a Responsible Federal Budget.

Many Democrats are furious with Obama, saying chained CPI represents bad policy and bad politics. Last week, lawmakers emerged from an information session arranged by House Minority Leader Nancy Pelosi (D-Calif.) complaining that their offices had been flooded with calls.

“Politically, this is not a winner. Our brand is the party that brought you Social Security,” said Rep. Rush D. Holt (D-N.J.), adding that his mother said she had heard that Obama was eliminating benefits for people older than 80. “We’ve now opened up the door for rumors about how Social Security will be reduced or eliminated. We don’t need that.”

Holt and others said Obama’s decision to offer the change now, before Republicans have made concessions on taxes, is a bad negotiating strategy. After the information session — featuring a supporter of Obama’s proposal, Robert Greenstein, president of the left-leaning Center on Budget and Policy Priorities, and an opponent, Damon Silvers, director of policy for the AFL-CIO — Pelosi said House Democrats agreed that chained CPI should be reserved for a broader discussion of Social Security solvency, not flipped casually onto the bargaining table in a debt-reduction deal.

“It’s too bad it’s in the budget,” Pelosi said.

Some Republicans are skeptical of the president’s motives, calling the offer a trap designed to lure Republicans into supporting not only Social Security cuts but also higher taxes. Of the $230 billion Obama proposes to save over the next decade by adopting chained CPI, about $100 billion comes from changes to the tax code. Because the income parameters for each tax bracket would rise more slowly, people would be thrown more quickly into brackets with higher rates.

“This means the Obama budget contains a tax increase on 10 percent of middle class taxpayers — anyone who pays the federal income tax,” the conservative Americans for Tax Reform said in a blog post. The group warned Republicans that supporting chained CPI would violate the ­anti-tax pledge of its founder, Grover Norquist.

The Club for Growth, another group that promotes conservative economic policies, threatened to find a primary opponent for Walden. President Chris Chocola noted that in 2005 “it was Republicans who said no” to President George W. Bush’s more ambitious plan to overhaul Social Security by adding private accounts.

“We have to reform entitlements, and this is a very minor measure,” Chocola said. “If you’re going to back away from this, you’re not serious.”

The White House and other analysts have argued that adopting the chained CPI is a more technical adjustment than genuine reform. The Bureau of Labor Statistics developed the measure after a commission led by Stanford University economist Michael Boskin concluded in 1996 that standard measures overstated inflation, in part because they did not account for the tendency to make substitutions between purchasing categories when prices rise. So although a grocery shopper’s switch from Honeycrisp apples to Gala, for example, would be covered, the switch from apples generally to bananas would not.

Over the past decade, the chained CPI has run about 0.3 percentage points lower per year than the traditional measure of inflation. Although the size of monthly Social Security checks would continue to grow, annual cost-of-living adjustments, or COLAs, would be slightly smaller than under current law.

Some argue that the chained CPI would cheat seniors by understating inflation for the elderly, who spend more on health care. The nonpartisan Congressional Budget Office has found conflicting evidence on that point. Still, to protect the very old, the White House proposes two bumps in benefits, one starting at age 76 and the other at age 95.

Even with those protections, the typical single elderly woman living on about $18,000 a year would lose about $6,000 by age 85 compared with current law, according to calculations by the National Women’s Law Center.

“She’s not making decisions about whether to buy steak or chicken. I testified about a woman — she can’t afford meat. She buys discount cheese and slices it very thin,” said the center’s Joan Entmacher. “I don’t know where you go from there in making substitutions.”

Charles Blahous, the Republican public trustee for Social Security, argues that the point of chained CPI “isn’t to provide a particular benefit level — it’s to adjust for general price inflation as we can best measure it.” Noting that recipients of disability benefits will face a 21 percent cut in three years, Blahous wrote, “Beneficiaries have much more to fear from leaving program solvency unaddressed than they do from technical corrections to the CPI.”

Rep. Sam Johnson (R-Tex.), who chairs the Social Security panel of the House Ways and Means Committee, has scheduled a first public hearing for Obama’s chained-CPI proposal on Thursday. The health subcommittee will follow with hearings on proposals to restrain the cost of Medicare.

Johnson praised Obama last week for including chained CPI in his budget request. The move, the 82-year-old congressman said, represents “a first step toward protecting Social Security for today’s workers.”