By the time she was 85, even with the bump-up, she would have a cumulative loss in benefits of almost $6,000 in today’s dollars. And by 94, the cumulative loss would be more than $8,300, according to the center’s calculations. But if she lived until 95, she would get the privilege of the second increase, also equivalent to 5 percent of the average benefit check. Her monthly check would climb back to the levels under the current law if she lived until 104, but by then, she would have lost about $10,200 in total income.

Of course, since the bump-up is a flat amount, some people with lower benefits might receive a bigger increase than they would under the current system, a senior administration official from the White House explained. Conversely, the bump-up offsets a smaller portion of the cut when benefits are higher.

This is not a popular move. According to a recent ABC News/Washington Post poll, 51 percent of respondents opposed changing the way Social Security benefits are calculated so that benefits increase at a slower rate, while 37 percent supported such a change (11 percent had no opinion). The survey said there were no partisan differences, but among people 65 and older opposition was 64 percent.

The “three-legged stool” of retirement — that is, pensions, savings and Social Security — has already become more of a lopsided two-legged stool, because pensions have been waning for years. And the Social Security leg is providing most of the support for many retirees: about 43 percent of single people and 22 percent of married couples rely on the benefits for more than 90 percent of their income, the Social Security Administration says. More than half of couples and 73 percent of singles draw more than half their income from the program.

The new measure of inflation would alter the way their benefits increase. Right now, Social Security is pegged to the C.P.I.-W, which tracks the typical purchases of a sample of urban wage and clerical workers, but does not include retirees. (Social Security uses this index because it was the only one that existed when the benefits were first adjusted for inflation.) The chained C.P.I.-U includes some retirees.

The chained C.P.I. would more broadly account for how people change their buying habits when prices rise, substituting cheaper items for more expensive ones. When the price of Porterhouse steak increases, the current index considers that a consumer can switch to a cheaper cut, as explained in an AARP paper. But the chained index would account for substitution between category types. So instead of buying cheaper beef, the consumer might switch to chicken.

But critics argue that the elderly and disabled do not have the ability to substitute as much as other consumers. “When so much of their budget goes toward health care expenses,” said Cristina Martin Firvida, director of financial security at AARP, “you are not going to choose to replace a hip treatment with another treatment just because it is cheaper. There is a limit for substitution with older people. We already account for a great deal of it in the current calculation.”