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. ||||| Speaker John Boehner (R-Ohio) on Friday said he was not concerned about losing his Speakership, a day after House Republicans refused to support his fallback plan to avoid most of the fiscal cliff. 
 
 
 
 “No, I’m not,” Boehner said in response to a question at a Capitol press conference, where he was joined by his chief lieutenant, Majority Leader Eric Cantor (R-Va.). 
 
 
 
 
 
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 The Speaker suffered the most embarrassing defeat of his two-year tenure on Thursday when he was forced to cancel a planned vote on legislation that would have allowed tax rates to rise on family income over $1 million.Boehner, who sent the House home for Christmas, said it was up to President Obama and the Democratic-led Senate to act to prevent a set of painful tax increases and spending cuts from taking effect beginning Jan. 1.He said he would continue working with the president and other congressional leaders on a broad deficit reduction agreement, but he said plainly he did not know what it would be. “How we get there, God only knows.”In response to direct questions, Boehner refused to rule out an eventual House vote on legislation that would garner mostly Democratic votes. The Senate earlier this year passed a bill extending tax rates for family income up to $250,000, but Boehner said it was invalid because legislation that raises revenue cannot, under the Constitution, originate in the Senate.“There is no Senate bill that has come to the House,” he said. “As we all know, the Senate bill had a blue-slip problem and continues to sit in the United States Senate. So we don’t have a Senate bill.”The Speaker reiterated that the House in August passed legislation to extend all current tax rates and replace the automatic spending cuts, but the Senate has already rejected that proposal.Boehner insisted he was not walking away or abandoning the possibility of a year-end deal, even though the House has recessed for Christmas. “We’re prepared to come back if needed,” he said.In brief remarks, Cantor echoed Boehner’s message.The Speaker attributed Thursday’s setback to “a perception” that his proposal raised taxes, an assessment he said he did not share. The legislation did not explicitly increase tax rates, but for years before the November election, Republicans, including party leaders, had argued that such proposals when offered by Democrats were de facto tax hikes.Boehner said he was “proud” of his members and did not interpret the rejection of his bill as a personal rebuke.“Listen, you’ve all heard me say this, and I’ve told my colleagues, if you do the right things everyday for the right reasons, the right things will happen,” he said. “While we may have not been able to get the votes last night to avert 99.81 percent of the tax increases, I don’t think … They weren’t taking that out on me. They were dealing with the perception that someone might accuse them of raising taxes.”And with that, Boehner reportedly offered a hearty “Merry Christmas, everyone!” and left the room. ||||| President Barack Obama issued a stern summons to congressional leaders Friday to approve legislation before year's end to prevent tax increases on millions of middle class Americans and prevent an expiration of long-term unemployment benefits for the jobless. 
 
 Speaker John Boehner of Ohio, center, departs, with reporters nearby after a House Republicans meeting on Capitol Hill, Thursday, Dec. 20, 2012 in Washington. Confronted with a revolt among the rank and... (Associated Press) 
 
 President Barack Obama speaks to reporters about the fiscal cliff in the Brady Press Briefing Room at the White House in Washington, Friday, Dec. 21, 2012. (AP Photo/Charles Dharapak) (Associated Press) 
 
 Speaker of the House John Boehner, R-Ohio, speaks to reporters about the fiscal cliff negotiations at the Capitol in Washington, Friday, Dec. 21, 2012. Hopes for avoiding the "fiscal cliff" that threatens... (Associated Press) 
 
 House Minority Leader Nancy Pelosi, D-Calif., meets with reporters about the fiscal cliff negotiations at the Capitol in Washington, Friday, Dec. 21, 2012. She is joined by House Minority Whip Steny Hoyer,... (Associated Press) 
 
 Speaker of the House John Boehner, R-Ohio, joined by House Majority Leader Eric Cantor, R-Va., left, speaks to reporters about the fiscal cliff negotiations at the Capitol in Washington, Friday, Dec.... (Associated Press) 
 
 President Barack Obama waves as he leaves the podium after speaking about the fiscal cliff in the Brady Press Briefing Room at the White House in Washington, Friday, Dec. 21, 2012. (AP Photo/Charles Dharapak) (Associated Press) 
 
 Speaker of the House John Boehner, R-Ohio, speaks to reporters about the fiscal cliff negotiations at the Capitol in Washington, Friday, Dec. 21, 2012. Hopes for avoiding the "fiscal cliff" that threatens... (Associated Press) 
 
 One day after House anti-tax rebels torpedoed Republican legislation because it would raise rates on million-dollar-earners, Obama said he still wants a bill that requires the well-to-do to pay more. "Everybody's got to give a little bit in a sensible way" to prevent the economy from pitching over a recession-threatening fiscal cliff, he said. 
 
 He spoke after talking by phone with House Speaker John Boehner _ architect of the failed House bill _ and meeting with Senate Majority Leader Harry Reid. 
 
 "I still think we can get it done," Obama said as he struggled to pick up the pieces of weeks of failed negotiations and political maneuvering.
– Today's fiscal cliff developments have a familiar ring: More talk, no solutions. But while no miracles emerged from Capitol Hill, President Obama took to his podium to declare, "I still think we can get it done." He wants lawmakers to come back after the holiday to pass a scaled-down deal before year's end that protects most Americans from a tax increase and lays the groundwork for more comprehensive legislation, reports AP. Earlier, John Boehner said he would continue working toward a deal in the wake of his own "Plan B" meltdown, but added, "How we get there, God only knows," reports the Hill. Obama made the case that because Democrats and Republicans alike agree that the vast majority of Americans should be saved from a tax hike, "there is absolutely no reason, none," not to make it happen before the deadline 10 days from now. "Call me a hopeless optimist," he said, adding that he spoke with both Boehner and Harry Reid today. One plan in the works among Democrats is a proposal to extend tax cuts for those making below $250,000, extend unemployment benefits, and temporarily suspend automatic spending cuts, reports the New York Times.