Obama had included a chained CPI proposal in his budget last year. On Thursday, the White House said it would not be in his upcoming budget, due March 4.
Many economists say chained CPI is a more accurate way to measure inflation because it corrects for biases in more widely used measures. In particular, it assumes consumers will substitute what they usually buy - e.g. a steak - with a similar but lower priced item - such as hamburger meat - when the price of steak goes up a lot.
On average, chained CPI is expected to grow 0.25% to 0.3% slower than the current CPI measure, according to the Committee for a Responsible Federal Budget.
But economists' argument didn't win over the liberals.
"'Chained CPI' is a fancy term for a boneheaded idea: ... In the wealthiest nation on earth, there is simply no excuse for more cuts that harm the most vulnerable among us. [We] thank the President for listening to the concerns of his constituents," MoveOn.org, the progressive activist group, said Thursday.
A switch to chained CPI would affect Americans in other ways.
It would slow the growth rate in all federal payments that are adjusted annually for cost of living. These include pensions for civilian worker and the military, veterans' benefits, and Pell Grants.
It would also slow changes to tax parameters that go up with inflation -- and that could mean somewhat higher taxes for many.
The switch to chained CPI could reduce deficits by $233 billion over a decade, the Congressional Budget Office estimated last year.
Though it won't be in the official budget proposal, chained CPI remains "on the table," according to a White House official, but only as part of a deal that asks the wealthy to sacrifice something as well.
"Over the course of last year, Republicans consistently showed a lack of willingness to negotiate on a deficit reduction deal, refusing to identify even one unfair tax loophole they would be willing to close, despite the President's willingness to put tough things on the table," the official said.
Republicans took a different view.
"This reaffirms what has become all too apparent: the president has no interest in doing anything, even modest, to address our looming debt crisis," said Brendan Buck, the press secretary for House Speaker John Boehner.
Neither side noted it's a mid-term election year, when expectations are low that any progress will be made on any major issue.
- CNN's Paul Steinhauser contributed to this report