Sen. Lindsey Graham (R-SC) thinks it's time to take the fight directly to Libyan leader Col. Muammar Gaddafi regardless of what the U.N. mandate says.

"The military's strategy of taking U.S. air assets out of NATO, I think, was a big mistake," Graham told CNN's Candy Crowley Sunday.

"My recommendation to NATO and the administration is to cut the head of the snake off, go to Tripoli, start bombing Gaddafi's inner circle, their compounds, their military headquarters in Tripoli. The way to get Gaddafi to leave is have his inner circle break and turn on him. 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."

"Here's the problem," Crowley noted. "The U.N. resolution calls for protecting the Libyan people. It is going to be hard to make that connection saying, 'Listen, we're going after Gaddafi, we're going after his men.' That is not within the mandate."

"Well, it is my belief that it is going to be hard for American national security interests to survive intact if Gaddafi stays," Graham said. "You know, I like coalitions. It is good to have them. It is good to have the U.N. involved. But the goal is to get rid of Gaddafi, a military stalemate is ensuing and the only way I know to make this thing successful is to put pressure on Tripoli. The people around gadhafi need to wake up every day wondering will this be my last. The military commanders in Tripoli supporting Gaddafi should be pounded."

"So I would not let the UN mandate stop what is the right thing to do," he added.

Watch this video from CNN's State of the Union, broadcast April 24, 2011.

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