Rep. Mike Rogers, R-Ala., one of several Republicans who left the meeting before it concluded, said Obama told Republicans he is concerned balancing the budget would require spending cuts so deep they would slow the economic recovery, Roll Call reported.
Rep. Paul Broun, R-Ga., who also left while the meeting was still in progress, said Obama's remarks show the president is not willing to balance the budget, Roll Call reported.
White House press secretary Jay Carney said Wednesday Obama's offer to use the so-called chained CPI to calculate annual adjustments in Social Security benefits "demonstrates the seriousness with which he approaches this challenge, the seriousness with which he believes -- the seriousness with which he approaches the necessity of bipartisan cooperation and his willingness to make tough choices in an effort to find common ground."
Obama told ABC News in an interview that aired Wednesday there are only "a finite number of changes that could be made to deal with our deficit" and the federal government "can actually put in place a growth strategy that creates jobs and protects the middle class and helps them thrive and grow."
Liberal U.S. senators challenged Obama over his readiness to cut entitlement benefits, as the president prepared to meet with House Republicans.
"I think he is more inclined to cut benefits, which I strongly disagree with," Sen. Bernie Sanders, Ind-Vt., said Tuesday after leaving a 90-minute, closed-door Senate Democratic Caucus meeting with Obama on Capitol Hill that focused a lot on Social Security and Medicare benefits.
The meeting also dealt with immigration policy, drones and cybersecurity, Senate attendees said.
Sanders and Sen. Tom Harkin, D-Iowa, told Obama they opposed his willingness to consider adopting chained CPI -- a less generous formula than the one currently used for adjusting benefits under Social Security and other programs for inflation.
The Bureau of Labor Statistics' chained CPI, or a chained consumer price index, is not used by Washington but has increasingly been discussed as a reform because many economists say it better measures inflation than the currently used CPI index.
It tweaks the inflation formula slightly but results in big savings over the long run, perhaps more than $100 billion over a decade, The Washington Post reported. It also reduces the federal deficit through a combination of spending cuts and increased revenues.
Obama has said he is open to chained CPI as part of a "grand bargain" that would include spending cuts as well as new revenue.
And he didn't back down from that position during Tuesday's meeting, those in attendance said -- a position that raised the hackles of the caucus' liberal wing, especially Harkin and Sanders.
"My point and Bernie Sanders' point was when you're talking about entitlements -- Social Security and Medicare -- there's more than one way to solve that problem," Harkin told reporters.
He said Obama's response was that "things were open for negotiation" but that he wanted to reach a grand bargain.
Sen. Carl Levin, D-Mich., said Obama "thinks it's very important that we solve these problems together and he said that working together with Republicans in terms of getting a grand bargain or a major dent in this issue [of cutting the deficit] is critically important.
"But compromise is essential and he hasn't seen enough of it from them, but he's also going to continue trying," Levin said.
Obama is to meet with House Democrats and Senate Republicans in separate sessions Thursday.