President Barack Obama can’t count on his left flank to support his entitlement changes just because he’s not raising the Medicare eligibility age.

Progressives say the latest deficit-cutting proposal in the fiscal cliff negotiations would unfairly put the squeeze on seniors — largely because a new formula for calculating Social Security payments would fail to account for how much more money they have to spend on health care than the rest of the population.

(Also on POLITICO: What is chained CPI?)

And that unless the proposed Social Security payment cuts are offset for older, low-income seniors, they’re worried that this vulnerable group could be forced into choosing between necessities — between housing, for instance, and medical care.

“If we don’t do this right, we could be asking old, poor elderly people to make some pretty terrible choices,” said Jared Bernstein, former economic adviser to Vice President Joe Biden and now a senior fellow at the Center on Budget and Policy Priorities. “And there’s no reason or need for the richest country in the world to treat people that way.”

(PHOTOS: Fiscal cliff's key players)

In the latest development in the fiscal cliff talks Monday night, Obama agreed to tweak the way some government benefits and income tax brackets are calculated, switching to what’s called the chained consumer price index. The effect would be to slightly slow the increase of cost-of-living adjustments in Social Security and to move people slightly more quickly into higher tax brackets.

Obama’s offer estimates it would cut the deficit by $135 billion over 10 years.

It’s an idea embraced by many of the prominent deficit-reduction proposals — including Simpson-Bowles, Domenici-Rivlin and the Gang of Six. The reason? Economists generally agree that it’s a more accurate way to calculate inflation, mainly because it takes into account people’s tendency to buy cheaper substitute goods — chicken, for instance — if the cost of beef goes up. The CPI that’s used now doesn’t do that.

The conservative Heritage Foundation supports it, too, including it in its “Saving the American Dream” report. In a blog post, Heritage’s David John wrote that a chained CPI would be a “more accurate measure” of how people’s spending habits actually change. The change, he wrote, “is not nearly enough to fix Social Security’s massive deficit, but it is a good start.”