Muammar Qaddafi's hold on power could be getting more tenuous by the hour.

Allied air strikes reportedly targeted his compound in Ajdabiya Wednesday. Coalition planes also bombed Qaddafi's forces in Misrata, to stop them from shelling civilians.

Defense Secretary Robert Gates says he can't predict how long the operation will last, but said the U.S. could transfer control to allies by Saturday.

Meanwhile, House Speaker John Boehner wrote to President Obama to complain that the mission's goals are not clearly defined.

CBS News correspondent Mark Phillips reports from Tripoli that the combined coalition air forces have declared something like victory.

"Effectively, their air force no longer exists as a fighting force, and his integrated air defense system and command and control networks are severely degraded to the point that we can operate with near impunity across Libya," said Air Vice-Marshall Greg Bagwell of the British Royal Air Force.