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.

It would mean smaller annual increases in Social Security payments, government pensions and veterans’ benefits. 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 antipoverty programs like Medicaid, Head Start, food stamps, school lunches and home heating assistance because annual adjustments to the poverty level would be smaller, leaving fewer people under the official poverty line.

House Republicans proposed the new inflation measure Monday as part of a 10-year, $2.2 trillion plan to avoid the year-end fiscal cliff, a combination of automatic tax increases and spending cuts that economists warn could send the economy back into recession. They also proposed raising the eligibility age for Medicare from 65 to 67, and raising taxes by $800 billion.

President Barack Obama supported the new inflation measure in deficit-reduction talks last year. That increases the possibility it could become part of a compromise, though White House officials have said they oppose including changes to Social Security in the current talks.

Obama sidestepped the issue when he was asked about it in a broadcast interview Tuesday.

“I am willing to look at anything that strengthens our system and makes it, and makes it clear over the long term that the basic social safety net for our seniors is going to be there,” Obama said on Bloomberg Television.

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.

The chained CPI assumes that as prices rise, consumers turn to lower-cost alternatives, reducing the amount of inflation they experience. For example, if the price of beef increases while the price of pork does not, people will buy more pork. Or, as opponents argue mockingly, if the price of home heating oil goes up, people will turn down their heat and wear more sweaters.

The new inflation measure is unpopular among many Democrats in Congress and advocates for seniors who complain that it would disproportionately hit low-and middle-income families. AARP and other groups have been fighting it for years.

“Think about it this way. You’re standing on the deck of a boat and you’re in very deep water and they want you to swim but they are going to put a log chain around your foot. That’s chained CPI,” Sen. Tom Harkin, D-Iowa, said at a recent rally on Capitol Hill to oppose cuts to benefit programs. “One way or the other it’s going to drag you to the bottom.”

But the new inflation measure is popular among budget hawks in part because it cuts benefits and increases taxes gradually in ways that might not be readily apparent to most Americans. The savings, however, become substantial over time, adding up to more than $200 billion over the next decade, according to congressional estimates.

“It’s a proposal with bipartisan support because it more accurately reflects the changes in costs,” said Michael Steel, spokesman for House Speaker John Boehner, R-Ohio.

Overall, the proposal would cut Social Security benefits by $102 billion over the next decade, according to an estimate by the nonpartisan Congressional Budget Office. It would cut government pensions and veterans’ benefits by $21 billion over the same time period. Supplemental Security Income, the disability program for the poor, would be cut by nearly $7 billion

For the more than 56 million people who get Social Security, the new measure would reduce annual cost-of-living adjustments, or COLAs, by an average of 0.3 percentage points each year, according to the Social Security Administration. Next year’s increase is scheduled to be 1.7 percent. Under the chained CPI, it would be about 1.4 percent.

“Seniors who on average get about $14,000 in Social Security benefits a year are going to get, on average, about a $21 a month increase in their benefits to pay for all the increased costs of their medicine, increased cost of their rent, increased cost of daily living — $21 a month,” said Rep. Xavier Becerra of California, the top Democrat on the House Ways and Means Social Security subcommittee. “Republicans are saying in their proposal we must cut that cost of living increase for America’s Social Security recipients who paid for those benefits.”

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 would cut Medicaid, the health insurance program for the poor, by $12 billion over the next decade. Medicare, the health insurance program for seniors, would see savings of almost $9 billion.

Taxes, however, would rise by about $65 billion over the same period.

The tax increases would hit low-income families the hardest, while high-income taxpayers would see smaller changes, according to a 2011 analysis by the nonpartisan Joint Committee on Taxation, the official scorekeeper for Congress.

For example, by 2021, taxpayers making between $10,000 and $20,000 would see a 14.5 percent increase in their federal taxes with a chained CPI, according to the analysis. Taxpayers making $200,000 to $500,000 a year would get a tax increase of 0.2 percent. People making more than $1 million would get a tax increase of 0.1 percent.