Burgeoning liberal anger over a plan to lower Social Security cost-of-living increases as part of a fiscal cliff deal is having little effect on top Democrats, including Minority Leader Nancy Pelosi, D-Calif.

Pelosi, and others, are unlikely to push back against President Barack Obama’s embrace of the idea in his latest fiscal cliff offer to Speaker John A. Boehner, R-Ohio.

The proposal, called “chained CPI,” has provoked dissent among Democrats at the highest ranks. In a Tuesday meeting between House Democratic leadership and White House congressional liaison Rob Nabors, participants audibly groaned when Nabors broached Obama’s support for the plan.

But their concern was softened when Nabors explained several protections for poor and elderly seniors that the White House wants, according to a Democratic leadership aide. In fact, the White House is calling their proposal “superlative CPI,” which represents their modified version of a GOP-backed plan to change the way the Consumer Price Index is calculated in an effort to save the government money on entitlement payments.

Still, some high-ranking Democrats have panned the White House’s modifications. That includes Rep. Donna Edwards, D-Md., who was recently placed in charge of recruiting candidates at the Democratic Congressional Campaign Committee.

Even Democratic National Committee Chairwoman Debbie Wasserman Schultz, D-Fla., whom Obama recently picked to continue serving in her position, refused to say whether “chained CPI” counted as a “benefit” cut in an interview Thursday.

“We need to look at the total package,” she said about her view of the proposal. “You have to have a balanced plan.”

Among progressives, “chained CPI” is inspiring real anger, as it is viewed as one of the least palatable ways to cut spending in entitlement programs.

“It doesn’t make any kind of logical sense to me, except for the fact that the people who are pushing this think that they can make this comparatively economically weaker — and, therefore, politically less connected — group have to eat it,” said Rep. Keith Ellison, a co-chairman of the House Progressive Caucus.

Ellison, D-Minn., helped organize a recent letter with 102 signatures saying any changes to Social Security should be “off the table” in the fiscal cliff talks. Edwards organized another letter specifically against chained CPI that garnered 60 signatures.

Ellison and others are also whipping colleagues against a bill with the proposal in it.

A coalition of progressive outside groups is threatening to recruit primary challengers against Democrats who vote for a bill with “chained CPI,” and the groups have been directing thousands of activists to call Democratic members, including leaders.

But when asked about “chained CPI” Wednesday, Pelosi backed Obama, saying she considers it “a strengthening of Social Security.”

She did allow: “I’ve said to the members, ‘Express yourselves.’ Because I’m not thrilled with the president’s proposal.”

High-ranking Democrats said Pelosi is unlikely to back away from the idea, undercutting Obama in the fiscal cliff talks, as long as the contours of the deal stay close to Obama’s last offer.

“In the context of a large deal that reduces the deficit by a lot, that has a lot of revenue in it, all of which comes from the wealthiest and which has transportation jobs money, an extension of the debt ceiling for at least two years, a doc fix, a fix of the AMT, an extension of unemployment benefits — in that context, a chained CPI which has reasonable allowances for people with the least money, it’s something we don’t like but can support,” said Rep. Robert E. Andrews, a close ally of Pelosi’s.

“I’m highly confident that whatever the number of votes is that we need to pass an agreement like Rob Nabors outlined is, we will deliver,” Andrews said.

Pelosi specified that the additional protections Nabors outlined would include higher payments for low-income seniors and very old seniors.