That doesn't mean the fight against the health-care law should be abandoned, he said, adding that the measure will become a liability for the Democratic party.
"To our Democratic friends, you own Obamacare and it's going to be the political gift that keeps on giving," he said. "So the shutdown will be old news next year; Obamacare's faults will be front and center in 2014, if we don't screw this up."
And Graham wasn't alone. Sen. Kelly Ayotte (R-N.H.) echoed his sentiment on CBS's "Face the Nation."
"I believe that the defunding strategy was a failed strategy from the beginning," she said.