It shouldn’t come as a surprise that the GOP was asking to trim the growth of Social Security benefits in a fiscal cliff deal — they’ve been demanding spending cuts for two years and President Barack Obama had already put it on the table, most recently in his Sunday interview on “Meet the Press.”

But that offer — made before Christmas — was part of a grand bargain, one that would include a long-term debt limit hike and far more revenue, $1.3 trillion as opposed to the less than $1 trillion the government would get from not extending the Bush-era tax cuts for the wealthy.

Senate GOP leaders on Saturday night included a new inflation index, called a “chained CPI,” in their offer for a stop-gap measure mainly aimed at averting tax hikes on the middle class. The move struck many Democrats as a colossal overreach.

According to the Congressional Budget Office, moving to the chained consumer price index would save $112 billion over 10 years by reducing the growth in Social Security benefits paid to retirees and people with work-related disabilities. Another $72 billion would come from new revenue because a lower inflation rate is likely to move many households more easily into higher tax brackets, which are pegged to inflation.

Democratic leaders weren’t about to trade away Social Security on the cheap, as Senate Majority Leader Harry Reid, D-Nev., made clear on the Senate floor Sunday afternoon. That was shortly after he admitted he was unable to counter the GOP’s offer with a unified Democratic proposal.

Republicans backpedaled furiously late Sunday, as soon as it became apparent that the chained CPI proposal was being cast by Democrats as a “poison pill.”

Sen. Lindsey Graham of South Carolina said he counted 80 senators who were ready to vote for a plan that did not include chained CPI. Republican Sens. Bob Corker of Tennessee, John McCain of Arizona, Olympia J. Snowe of Maine and others also said it did not need to be in the fiscal cliff deal.

“Report that #GOP insisting on changes to social security as part of #fiscalcliff false,” Sen. Marco Rubio of Florida posted on Twitter. “BTW those changes are supported by @barackobama.”

The chained CPI has a long history that has been embraced at least in some form by some liberal economists as well as conservative ones as a way to slowly trim Social Security and other benefits to make them more affordable and to more accurately portray rising costs.

But for leading liberals in the Senate, such as Sens. Tom Harkin of Iowa and Bernard Sanders of Vermont, it’s nothing more than a benefit cut to pay for more tax cuts. Any deal that includes Social Security cuts will lose Democratic votes as a result. Still, the odds remain high that the proposal will soon become law; if not in this package then in a bipartisan package in a few months to extend the debt ceiling.

With Obama having already walked away from the other headline benefit cut he tentatively backed during the 2011 grand bargain talks — raising the Medicare eligibility age to 67 — the chained CPI is the biggest remaining trophy he has left to offer up to the GOP in any long-term deal.

Emily Holden and David Harrision contributed to this report.