Those talks failed but the idea could resurface as policymakers look for ways to cut benefits to improve the program’s finances and reduce federal spending.

Mitt Romney, Obama’s Republican opponent in the presidential election, says he would strengthen Social Security by slowing the growth of benefits for people with ‘‘higher incomes.’’ Romney hasn’t defined ‘‘higher incomes’’ or explained how he would slow the growth of benefits for such people.

One way would be to reduce their annual COLAs.

Advocates for seniors are fighting back in ad campaigns and at local forums across the country. They say this year’s small pay hike is evidence that the COLA shouldn’t be shrunk.

‘‘Seniors know all too well their living costs often far outpace the COLA increase, yet incredibly many politicians are proposing a new formula that will erode this inflation protection even more,’’ said Max Richtman, who heads the National Committee to Preserve Social Security and Medicare.

‘‘It’s hard to imagine how anyone can argue the current COLA is too generous,’’ Richtman said. ‘‘I've asked seniors at town hall meetings nationwide how many think the COLA is too large — laughter is always the response.’’

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