Democrats are balking at President Barack Obama’s latest offer to House Republicans to shift the way inflation is calculated.

The White House proposal presented a tough choice for Democrats, who have long criticized the new inflation measure as a thinly veiled attempt to reduce entitlement benefits for the poor and elderly.

Part of the broader White House offer on the fiscal cliff of tax and spending measures, the plan would apply the new inflation index, called “chained CPI,” to the Social Security Administration and the tax code.

Democrats sharply criticized the idea on Capitol Hill on Tuesday, but several said they hoped the White House could create a cushion to soften the impact on the neediest beneficiaries.

“I don’t like it at all,” said Sen. Sherrod Brown, D-Ohio, adding that his colleagues “overwhelmingly” agreed with him on the issue.

“I’m not going to draw any line in the sand,” said Sen. Benjamin L. Cardin, D-Md. “I’m going to fight hard to keep Social Security out of this.”

Sen. Jay Rockefeller, D-W.Va. said, “I won’t be happy about anything that happens to Social Security, Medicaid or Medicare.”

Still, Rockefeller said it didn’t mean he would vote against an ultimate deal.

Rep. Sander M. Levin of Michigan said his “strong preference” would be to leave chained CPI out of the deal. “I think there needs to be a further look at it and its potential impacts on the recipients,” he said. “As you know, it goes beyond Social Security. It covers veterans; it covers people with disabilities.”

There were no details in how the Obama administration might look to soften the impact, but officials said those plans could come late.

Sen. Ron Wyden, D-Ore., called the White House offer “fluid” and said he would reserve judgment until seeing more specifics.

“I want to see the details on the vulnerable,” he said. “That to me is kind of the threshold question in order to have the debate.”

White House Legislative Director Rob Nabors addressed Democratic senators about the White House offer, but Sen. Richard J. Durbin, D-Ill., said Nabors “didn’t get into specifics.”

Including the chained CPI in the offer represents a major concession by Obama, who had previously joined Hill Democrats in saying he would not accept any plan that reduced benefits to retirees. Boehner’s earlier offers both had a government-wide inflation change.

White House spokesman Jay Carney said Tuesday that the idea of shrinking the annual increase in payments came from Republicans and that Obama is trying to meet them halfway to get a broader deficit-reduction deal.

And, he said, the plan would have provisions that would hold the most vulnerable people harmless, although he had no details on how that would be accomplished.

Impact Spreads

According to the Congressional Budget Office, moving to the chained CPI would save $112 billion over 10 years by reducing the growth in Social Security benefits paid to retirees and people with work-related disabilities. Another $72 billion would come from new revenue because a lower inflation rate is likely to move many households more easily into higher tax brackets, which are pegged to inflation.

Many economists consider the chained CPI a more accurate measure of inflation because it takes into account the adjustments in consumption that people make in response to price changes.

But under chained CPI, the rate of inflation would rise more slowly than it does now. That means that people who receive government benefits adjusted to inflation would see their benefits grow more slowly each year than under the current method.

CBO says, for instance, another $33 billion could be generated by moving all government programs serving millions of people with disabilities, veterans or people in poverty onto the chained CPI. That would include roughly 8 million people who receive benefits from Supplemental Security Income, which helps low-income people with disabilities. Another 3.2 million people receive disability benefits from the Veterans Administration.

In recent weeks, advocates for people with disabilities and veterans had been getting increasingly vocal and pressuring lawmakers and the administration to spare them from potential future cuts.

“These are real people who at the end are going to be impacted by these actions,” said Curtis Decker, executive director of the National Disability Rights Network. Cutting benefits or changing the inflation measure “are going to impact people who are in pretty bad shape already.”

According to CBO, a person who retires at age 62 would be getting 3 percent less in benefits by age 73 under the chained CPI.

But people who receive disability checks from Social Security could feel more pain than retirees, said Monique Morrissey, an economist at the left-leaning Economic Policy Institute. “If you’re disabled at age 30, you’re going to be receiving benefits longer, and therefore the potential percentage decline in your benefits is greater,” she said.

Morrissey said it could have a double impact because federal poverty guidelines are pegged to inflation, so a stingier inflation measure may leave people ineligible for food stamps, school meals and other programs.

And neither the current inflation measure nor the chained CPI takes into account that seniors and people with disabilities spend a greater share of income on health care expenses, which rise much faster than inflation, she said. “What’s really behind this is an attempt to raise revenues on the one hand and reduce benefits on the other in a stealthy fashion,” she said.

Still, analysts who support the measure say it would more accurately reflect the benefits that people are entitled to.

“There are not nearly enough wealthy people to solve the entitlement probably by taxing them,” said Jim Kessler, a co-founder of Third Way, a middle-of-the-road research group. “You can’t get there. There are some places where benefits are going to have to be trimmed to make sure these programs stay afloat.”

Ben Weyl and Steven T. Dennis contributed to this story.