Two of the Senate's foreign policy hawks disagree on whether the U.S. and NATO should directly target Libyan leader Moammar Gadhafi.

Sen. Lindsey Graham (R-S.C.) said Sunday the best way to end the conflict in Libya, which appears to be heading toward a stalemate, is to take out the leadership.

"My recommendation to NATO and the administration is to cut the head of the snake off, go to Tripoli, start bombing Gadhafi's inner circle, their compounds, their military headquarters in Tripoli," he said on CNN's "State of the Union."

"I would not let the U.N. mandate stop what is the right thing to do. You cannot protect the Libyan people if Gadhafi stays," he added. "You cannot protect our vital national security interests if Gadhafi stays. The long, drawn-out, protracted engagement is not good for the Libyan people."

But Sen. John McCain (R-Ariz.), who is advocating for the U.S. to retake a leadership role in the NATO operation, said that strategy will not work.

"We have tried those things in the past with other dictators, and it’s a little harder than you think it is," McCain said on CNN. "Gadhafi is a survivor, and we don’t know exactly where he is. We do have to worry about civilian casualties, that could turn the Libyan people against us."

McCain did say he agrees with Graham that Gadhafi should not feel safe.

"We can’t count on taking Gadhafi out — what we can count on is a trained, equipped, well-supported liberation forces which can either force Gadhafi out or obtain victory," McCain said. "My emphasis is winning the battle on the ground, not taking him out with a lucky air strike."