WASHINGTON — President Barack Obama’s offer to limit the growth of Social Security benefits would cost the average retiree less than $50 in the first year. But the cuts would grow over time, and that has advocates for senior citizens worried that Democrats in Congress will break their promise to shield the retirement and disability program from cuts in deficitreduction talks.

Senate Majority Leader Harry Reid, D-Nev., and House Minority Leader Nancy Pelosi, D-Calif., pledged not to touch Social Security as part of negotiations to avoid the year-end “fiscal cliff.” Reid, however, is backpedaling now that Obama and House Speaker John Boehner, R-Ohio, have agreed to a new measure of inflation that would reduce annual cost-ofliving adjustments, or COLAs, for Social Security and othergovernment programs.

Obama and Boehner continue to haggle over how much to raise taxes and cut spending, but both have agreed to the new inflationmeasure formula, making it increasingly likely the proposal would be part of an eventual deal. Boehner proposed the change earlier this month in talks with Obama, and the president included it in a counteroffer this week.

White House press secretary Jay Carney called the new inflation measure a technical adjustment designed to make inflation estimates more accurate. Obama did not directly address the issue at a White House news conference Wednesday. But, he said, a deal will require difficult choices by all sides.

“What I’ve said is that in order to arrive at a compromise, I am prepared to do some very tough things, some things that some Democrats don’t want to see and probably there are a few Republicans who don’t want to see either,” Obama said.

The inflation measure under consideration is called the Chained Consumer Price Index. On average, the measure shows a lower level of inflation than the more widely used Consumer Price Index because it assumes that as prices rise, consumers turn to lower-cost alternatives, reducing the amount of inflation they experience.

If adopted across the government, the change would have far-reaching effects because so many programs are adjusted each year based on year-to-year changes in consumer prices.

Taxes would slowly increase because annual adjustments to income-tax brackets would be smaller, pushing more people into higher tax brackets. Over time, fewer people would be eligible for anti-poverty programs such as Medicaid, Head Start, food stamps and school lunches because annual adjustments to the poverty level would be smaller, leaving fewer people under the official poverty line.

On average, annual increases in Social Security payments, government pensions and veterans benefits would be about 0.3 percentage point smaller each year. Next year’s cost-of-living adjustment is 1.7 percent, or about $21 a month for the average Social Security retiree. If the new measure of inflation were in effect, the costof-living adjustment would be about 1.4 percent, or a little more than $17 a month. That’s $4 less than the current system, or about $48 less during the course of a year.

Once the change is fully phased in, yearly Social Security benefits for a typical middle-income 65-year-old would be about $136 less, according to an analysis of Social Security data. At age 75, annual benefits under the new index would be $560 less. At 85, the cut would be $984 a year.

“The Chained CPI is a stealth benefit reduction that will compound over time and cut thousands of dollars in retirement income for current beneficiaries,” said Nancy LeaMond, AARP’s executive vice president.

More than a dozen veterans groups gathered Wednesday on Capitol Hill to oppose the change, which also would affect retirement and disability benefits for veterans.

“It is very easy to say you support the troops,” said Tom Tarantino, chief policy officer of the Iraq and Afghanistan Veterans of America. “But what many don’t get is that that support for the troops doesn’t stop when a shipment of guns hits the ground in Afghanistan. It is a promise you made to every man and woman who serves in the military, from the time they raise their hand to the timethey die.”

Sen. Bernie Sanders, a Vermont independent who organized the gathering of veterans, said, “We must do deficit reduction, but not by cutting programs for people who lost arms, legs and eyes defending our country.”

If enacted for 2014, the change would reduce government borrowing by $223 billion over the next decade - $158 billion in spending cuts and $65 billion in tax increases, according to the nonpartisan Congressional Budget Office. The biggest savings - $102 billion - would come from Social Security.

Reid had been adamant that Social Security should not be included in deficit-reduction talks.

In November, Reid told reporters: “I’ve made it very clear. I’ve told anyone that will listen, including everyone in the White House, including the president, that I am not going to be part of having Social Security as part of these talks relating to this deficit.”

On Tuesday, Reid sidestepped a question about it.

“This isn’t going to be a situation where we’re going to vote on a particular provision in the bill,” Reid said. “It’s going to be a framework to do something about the long-term security of this country.”

Front Section, Pages 7 on 12/20/2012