Graham was joined on CNN's "State of the Union" by Sens. John McCain, R-Ariz., and Joe Lieberman, Ind-Conn.
Graham said coalition forces should "cut the head of the snake off."
Libya "looks like a stalemate," Graham said. "The military's strategy of taking U.S. air assets out of NATO I think was a big mistake. I'm glad the Predator drones are going to be used.
"The way to get Gadhafi to leave is have his inner circle break and turn on him," Graham said. "And that's going to take a sustained effort through an air campaign. I think the focus should now be to cut the head of the snake off. That's the quickest way to end this."
McCain, who made a surprise visit to Libya last week, said Gadhafi is able to keep some members of his military loyal by paying them large sums of money. He also called for help in arming the rebels seeking Gadhafi's ouster.
"I visited the army base outside of Benghazi also on Friday, and they have a long, long way to go as far as training and equipment is concerned," McCain said. "So they're badly outgunned."
Lieberman said he has no concerns over the use of Predator drones in Libya.
"I mean we're in the fight and the political goal is to get Gadhafi out and to help the freedom fighters achieve their own independent for Libya," Lieberman said. "And therefore I think the use of our Predator drones, which have extraordinary capabilities, was the right thing to do. And I thank President Obama as commander in chief for authorizing that to happen."