WASHINGTON — As part of a deal being negotiated by President Obama and Speaker John A. Boehner to avert the worst of the year-end tax increases and spending cuts, Social Security payments might be lower in the future for millions of Americans.

On Tuesday, Democrats and Republicans were examining a multitrillion-dollar deficit reduction package put forward by the president, though the two sides were trading barbed remarks and aides were emphasizing that nothing was final until the whole deal was done.

But the White House seemed willing to make a concession to Republicans with a switch in the formula that ensures that Social Security payments keep up with the pace of inflation — an idea that immediately proved unpopular with its liberal base.

“Any talk of shrinking the program to save money is flawed from the start because Social Security is not part of the national budget in the same way as military spending,” Representative Raúl M. Grijalva of Arizona said in a statement. “It’s paid for through a dedicated payroll tax separate from general budgeting.”

Manuel Balce Ceneta/Associated Press

Representative Charles B. Rangel of New York was among many on the left who echoed that sentiment. “Everyone has a grandparent, a friend or a neighbor who relies on the Social Security benefits they earned to pay for medical care, food and housing,” he said in a statement. “A move towards chained Consumer Price Index would be a long-term benefit cut for every single person who receives a Social Security check.”

Democrats and Republicans are considering switching Social Security payment adjustments to a “chained” Consumer Price Index. The Consumer Price Index tracks the price of a basket of commonly purchased household goods. A chained index accounts for consumers’ tendency to substitute similar items for one another as prices fluctuate. A consumer might buy more apples when the price of oranges increases, for instance.

Though it sounds like nothing more than a technical fix, adopting a chained index would squeeze benefits over time. The chained index ends up, in a given year, about 0.3 percentage points lower than the unchained index. That difference accumulates, so after five years, it might be 1.5 percentage points lower. Using a chained index would cut Social Security spending by about $112 billion over a decade, according to an estimate by the Congressional Budget Office.

AARP, the lobbying and research group for older Americans, immediately criticized the proposal. “We would rather see a broader discussion addressing retirement security,” said Debra Whitman, an executive vice president at AARP. “We object to the context in which it’s being discussed, which is a few weeks before Christmas, without people understanding what the change really means.”

Because the payment reductions would accumulate over time, AARP and other groups argue that they would hit the oldest Americans disproportionately hard. They might also unduly burden women, who tend to live longer than men, and the lowest-income older people, who are most dependent on Social Security checks, the groups warned.

Some economists and policy experts have also argued that both the current and the chained indexes underestimate the inflation that older Americans experience. The government produces an experimental “elderly index,” for instance, that tries to capture the consumption habits of people over 62 more accurately than other measures. For instance, older people buy more health care and less education than the average family, so the elderly index puts more weight on the former and less on the latter.

In no small part because of spiraling health care costs, inflation as measured by the elderly index has grown faster than inflation as calculated by the standard index that Social Security uses. That implies that the purchasing power of Social Security payments linked to a chained index would erode more over time, given what older Americans buy.

Jason Reed/Reuters

Still, other economists and policy experts from across the political spectrum have argued that a chained index is a more accurate measure of the inflation that households actually experience, and therefore is a better policy tool. They note that the elderly index is still experimental, and that not just older people receive or spend Social Security payments.

“We know that the current measure of inflation is not adequately measuring experienced inflation, and we should hence go with the better measure,” said Christian E. Weller, a senior fellow at the Center for American Progress, a liberal research group based in Washington, and the author of a plan to modernize Social Security.

Both liberals and conservatives have at times argued against making changes to Social Security outside the context of a broader overhaul. Many analysts — particularly Democrats — argue that Social Security does not contribute to long-term deficits because it has its own financing stream in payroll taxes. But it does have a long-term fiscal challenge, as payouts would eventually overwhelm its trust fund and revenues.

“Back when the system started, the demographics were really favorable,” said Andrew G. Biggs of the American Enterprise Institute, a right-leaning research group in Washington. “You could provide decent benefits for the rich and poor alike at low cost. You can’t do that anymore, mathematically. We could provide decent benefits for the rich and the poor by raising taxes a lot, but we need to raise taxes for other things.”

Mr. Biggs said Social Security changes that provided more ample benefits to vulnerable low-income older people and less to the well-off might prove to be a better path forward.

“We oppose chained C.P.I.,” Representative Peter Welch, Democrat of Vermont, said in an interview. “But I think all of us are waiting to see the details in the final package, and we’ll make our determination then.”

Correction: December 19, 2012

An earlier version of a caption in this post misstated Representative Raúl M. Grijalva’s affiliation. He is not affiliated with the American Enterprise Institute.