"President Obama claimed that Republican leaders are pushing to make 'privatizing Social Security a key part of their legislative agenda' should they regain control of the House and Senate," the group states in a release on Monday.
"We find the president's claim to be mostly false," it added.
The organization claims few, if any, Republicans now in Congress have pushed for privatizing the trust fund. It also states that there was little conservative support for the idea in 2005 when Republicans controlled both chambers on Capitol Hill and President George W. Bush was in the White House.
"Only one Republican leader is currently pushing publicly for Bush-style private accounts as part of an overall budget plan," FactCheck states.
Rep. Paul Ryan (R-Wis.), the ranking member of the House Budget Committee, has advocated this approach.
FactCheck claims Obama further distorted Republicans' position on the issue when he said the GOP would "[tie] your benefits to the whims of Wall Street traders."
"That's not true of the private accounts Bush proposed," the group states. "Those would have been invested in strictly regulated, broadly based mutual funds, much like the funds in which millions of federal workers invest their own retirement funds."
FactCheck.org is a nonpartisan, nonprofit organization that monitors claims by politicians and determines their accuracy. The group is a project of the Annenburg Public Policy Center at the University of Pennsylvania.
On Sunday, House Republican Chief Deputy Whip Kevin McCarthy (Calif.) told CNN that Democrats were using the Social Security issue to distract voters from the fact that their legislative initiatives have not stopped the economy from teetering on the brink of a double-dip recession.
"This is a scare tactic to try to get off jobs," he told CNN's "State of the Union." "Social Security isn't a fundamental problem. We should be able to sit down with both parties and start talking to make sure we secure it."