A top official at the nation’s largest union federation slammed a Social Security cut proposal that’s been floated by President Obama, but stopped short of calling it a deal-breaker in the next round of budget wars.

“We remain strongly opposed” to chained CPI, AFL-CIO government affairs director Bill Samuel told Salon. “It’s a very substantial benefit cut.”

“Chained CPI” is a proposed alternative method of calculating cost of living adjustments, which would reduce future increases in Social Security benefits. Samuel said that for many seniors on fixed incomes, even “the current system may not be adequate.” He called the claim that chained CPI could be implemented in a way that would be fair to such retirees “sort of ludicrous.”

Obama has repeatedly touted chained CPI as an aspect of a potential “Grand Bargain” with Republicans to reduce the deficit. In a “Meet the Press” interview aired on Dec. 30, the president highlighted it both as an example of his willingness to make concessions to the GOP and part of his “pursuit of strengthening Social Security for the long-term.”

The same day that interview aired, Republicans reportedly dropped their insistence on including chained CPI in the scaled-down so-called fiscal cliff deal, signaling they expect it to be part of a larger deficit deal in the next few months. So, it appears, does Obama. Can labor stop them?

“The White House has signaled many times they’re very open to this concept, which puts us in a very precarious situation,” said Eric Kingson, a co-chair of Strengthen Social Security. That coalition, whose 300-some member groups include the AFL-CIO and some of its largest unions, supports increasing Social Security benefits and opposes chained CPI, which Kingson called “a disguised benefit cut.”

Kingson and fellow co-chair Nancy Altman told Salon they would recommend that the Strengthen Social Security coalition oppose any overall deficit deal that includes chained CPI. Altman, whom the AFL-CIO is urging Obama to nominate as Social Security commissioner, said, “I think we would certainly have the view that there should be a line in the sand that should not be crossed.” But she noted that individual coalition members would “have to weigh a lot of things” in deciding whether their own groups would also support torpedoing an overall deal over chained CPI.