In remarks made during a debate that will air Sunday on South Carolina Educational Television, Jeff Duncan said Social Security should remain intact for those promised it, but not for those born today.
Democratic opponent Jane Dyer said the idea might sound good but "it's not going to work."
The two are seeking the 3rd Congressional District seat that represents the northwestern portion of the state. Four-term Barrett lost his bid to become governor in the GOP primary.
"Babies that are born today, I don't think we have that security net for them," said Duncan, 44, the owner of a real estate auction business. "We tell them, 'take personal responsibility.' We put some incentives in place for private retirement accounts and health care accounts."
Duncan said the proposal would make government "solvent in 60 or 70 years."
Dyer, a 52-year-old FedEx pilot and former Air Force captain, said the economic downturn has forced many in their 70s to seek employment in fast-food outlets and other minimum wage jobs because even Social Security won't make ends meet.
"It breaks our heart to see these people working like that at that age. We're deciding now that we will do away with Social Security in the future?" Dyer asked. "If we continue America the way it is now, the middle class goes lower and lower and lower. ...Phasing out Social Security to me is a terrible idea. We have to figure out a way to make it work."
The two candidates also differed on extending tax cuts enacted under the Bush administration, term limits and immigration.
Dyer said she favors extending the Bush tax cuts for those who earn less than $250,000. Those who earn more will still get the cut for the first $250,000, but not beyond that, she said.
"If we let those tax cuts continue, it will cost us $3.3 trillion over the next 10 years and we can't afford that," Dyer said.
Duncan said he's in favor of keeping all the cuts, and eliminating the capital gains tax.
On term limits, Duncan said he would be in favor of limits of 8, 10 or 12 years in office.
"I will go to Washington, make an impact, and go home," said Duncan, who is in his fourth term as a member of the state House.
Dyer said the best term limitations are elections.
"They can kick me out two years from now," she said.
On immigration, Duncan said he favors a strict, anti-immigration law akin to Arizona's, and is opposed to allowing the children of illegal immigrants born in the United States to be recognized as U.S. citizens.
Dyer said the granting of citizenship is in the Constitution and she's not in favor of rewriting it. Trying to remove the millions of illegal immigrants would cost $1 trillion that the nation doesn't have to spare, Dyer said.