How, you ask, can these military actions rid Libya of Qaddafi without removing him by force? According to this New York Times article, the Obama administration is searching for a country that would be willing to take Qaddafi in, should he decide to leave Libya.
I did intentionally use the phrase "should he decide to leave Libya," because it doesn't seem like the NATO airstrikes are in any way meant to (or able to) force Qaddafi out. In fact, there is a disconnect in the goals of the NATO action and what Obama et al. see as the endgame, specifically a Gaddafi-free Libya.
The Times article quotes Benjamin J. Rhodes, deputy national security advisor, who said that the coalition has accomplished three major objectives: saving the rebel capital of Benghazi, setting up an international command to protect civilians, and providing humanitarian assistance. While these are fine objectives to accomplish if the goal is a rebel-held Benghazi, it is debatable if the current operations are helping the rebels anywhere else, much less making it harder for Qaddafi to stay in Libya.
What this boils down to is that the status quo will not work in Libya. Obama, Cameron, and Sarkozy state in their article that allowing Qaddafi's rule to continue would be, "an unconscionable betrayal." Without an escalation of force, possibly even ground troops, there doesn't seem any way for the NATO allies to leave Libya without committing that betrayal. Unless, of course, Qaddafi decides to play nice and leave.