WASHINGTON — Once considered untouchable, Social Security is now in play in the debt-ceiling negotiations, which could mean higher income taxes for many U.S. families and shaved benefits for tens of millions of retirees as they age.

Social Security became part of the private discussions between President Barack Obama and Republican House Speaker John Boehner on coming up with “something big” to reduce deficits by $2 trillion to $4 trillion over the next decade.

Obama met with congressional leaders of both parties Thursday in the White House, their first session

to discuss the deficit cuts Republicans demand in return for voting to raise the government’s debt ceiling.

Obama called the meeting “very constructive” and said he would reconvene the eight leaders at the White House on Sunday after congressional and White House staff meet today and Saturday to hash out the details of everyone’s opening proposals.

“At that point,” Obama said, “the parties will at least know where each other’s bottom lines are and will hopefully be in a position to then start engaging in the hard bargaining that’s necessary to get a deal done.”

One option includes a new inflation measure for Social Security that could produce savings of close to $200 billion through a combination of reduced benefits and higher taxes, White House officials said Thursday.

Low- and middle-income families could be hit.

The proposal would represent a reversal for Obama. In contrast to his pledge to target tax increases at the wealthy, high-income families largely would be spared from tax increases that would result from changing the way inflation is measured.

And until now, the administration has been adamant that Social Security does not add to the deficit and should not be a part of deficit reduction talks.

Adopting a new inflation measure would allow policymakers to gradually cut benefits and increase taxes in a way that might not be readily apparent to most Americans.

There is no indication at this point whether Obama and congressional Republicans — and Democrats — will agree on the change. And, if they do, how broadly it might be applied. Another private meeting at the White House is set for Sunday.

The measure, if adopted across the government, would have a wide-ranging effect on taxes and government benefits, and those changes would grow over time.

The change would mean smaller annual increases in Social Security payments, government pensions and veterans’ benefits. Current payments would not be affected, but recipients would get smaller increases in the future.

Overall, the proposal would cut Social Security benefits by $112 billion over the next decade, according to the nonpartisan Congressional Budget Office. It would cut government pensions and veterans’ benefits by $24 billion over the same time period if adopted for them.

Reaction from the president’s own party was swift Thursday, raising questions about whether Obama can keep Democrats on board if he agrees to cuts in Social Security. House Democratic leader Nancy Pelosi said her caucus won’t support any package that includes Social Security cuts.

“Do not consider Social Security a piggy bank for giving tax cuts to the wealthiest people in our country,” Pelosi said. “We are not going to balance the budget on the backs of America’s seniors.”

AARP, the powerful lobby for seniors, “will not accept any cuts to Social Security as part of a deal to pay the nation’s bills,” said CEO A. Barry Rand.

The White House has been negotiating with congressional leaders over ways to reduce the government’s huge budget deficit as part of a deal to extend the nation’s ability to borrow. The government already has hit its $14.3 billion borrowing limit, and is in danger of defaulting on its obligations if the limit is not increased by Aug. 2.

White House spokesman Jay Carney said, “The president has always said that while Social Security is not a major driver of the deficit, we do need to strengthen the program.”

His statement did not address the possibility of reducing annual Social Security increases by changing the inflation adjustments.

In most years, Social Security payments are increased based on a measure of inflation called the Consumer Price Index for Urban Wage Earners and Clerical Workers. If Social Security adopted the new measure, annual increases would be 0.3 percentage points smaller, according to the program’s actuaries.

That could be a tough hit for seniors who have gone two years without a cost-of-living adjustment and are projected to get such a small one next year that it will probably be wiped out by higher Medicare Part B premiums for most recipients.

As the possible cuts are phased in, a typical 65-year-old who started receiving Social Security benefits at age 62 would get an annual reduction of about $130, according to an analysis of data produced by the Social Security actuaries.

By the time that retiree reached 75, the annual cut would be $560. At 85, the cut would be $984 a year.

Average Social Security benefits are about $1,100 a month, or about $13,000 a year.

“Social Security has contributed nothing to these deficits and to me has no basis for being a part of these deficit talks,” said Rep. Xavier Becerra of California, the top Democrat on the House Social Security subcommittee.

If applied more broadly to the tax code, the new inflation measure could hit taxpayers at every income level, raising about $60 billion over the next decade for the government, according to the nonpartisan Joint Committee on Taxation.