NATO targeted Libyan dictator Moammar Gadhafi's sprawling compound in Tripoli in a series of airstrikes on Monday.
The strikes destroyed a library and office and damaged a reception hall for visiting dignitaries. A security official said four people suffered mild injuries.
The military assault comes one day after pro-Gadhafi forces unleashed a barrage of shells and rockets on Misrata, the largest rebel-held city in the west.
Three members of the U.S. Senate Armed Services Committee say more must be done to drive out the Libyan strongman.
"I really fear a stalemate. I hope that Gadhafi goes. I hope that there's that kind of overthrow from within, but hope is not a strategy," Sen. John McCain, R-Ariz., said Sunday during a surprise visit to the North African country.
"The point is that we can't count on taking Gadhafi out," he continued. "What we can count on is a trained, equipped, well supported liberation forces, which can either force Gadhafi out or obtain victory and send him to an international criminal court."
"My emphasis is on winning the battle on the ground, not taking a chance on taking him out with a lucky air strike," McCain said.
Last week, President Obama authorized the use of American Predator drones in the fight. Some congressional leaders say that's a step in the right direction, but it is not enough.
"You know, you can't get into a fight with one foot," Sen. Joe Lieberman, I-Conn., said. "You got to get into it. 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."
Sen. Lindsey Graham, R- S.C., bluntly advised NATO and the Obama administration to "cut the head off the snake."
"Go to Tripoli, start bombing Gaddafi's inner circle, their compounds, their military headquarters in Tripoli," Graham said.
"The way to get Gaddafi to leave is have his inner circle break and turn on him," he added. "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."
Meanwhile, the coalition's airstrikes have delivered heavy blows to Gadhafi's army. But they have not been enough to halt his attacks on Misrata, a city of 300,000 people that has been besieged by Gadhafi loyalists for two months.