According to Obama, we are engaged in military operations in Libya because our principles and our interests justify (or require) us to be doing this. As far as the principles go, the idea seems to be that we are supposed to be keeping Qaddafi from slaughtering the rebels. As far as advancing our interests, there does seem to be a possibility that Qaddafi will be out and someone who might be more friendly to America will be in. Or maybe not.
Of course, to actually know whether we are acting in a principled way that also advances our self interest, we need to consider who we are supporting in Libya. Currently, the rebellion seems to be a disorganized affair with no central leadership. The rebels also seem to be poorly equipped and lacking in training (recent stories about the rebels include their firing a rocket the wrong way and not knowing how to use a mortar). There is also the fact that the rebels seem to be relatively few in number. As such, it would seem that we are backing a small number of poorly equipped and poorly trained rebels with no clear leadership who would certainly be defeated without our ongoing support.
Of course, that is not the full story. There have been indications that there are some competent combatants among the rebel forces. That is the good news, I suppose. The bad news is that they seem to be Al Qaeda and Hezbollah fighters. That is, one might imagine, bad news for the United States. Unless, of course, we want to get the band back together for an 80s reunion.
So, we are backing a small number of poorly equipped and poorly trained rebels with no clear leadership whose few competent combatants appear to be enemies of America. This does not sound like an ideal situation.
To address some of these problems, the CIA has been active in the region and there are plans to provide them with arms and presumably training. Meanwhile we will presumably keep providing support via our military operations. I can only assume that we are hoping some sort of leadership will emerge and that more of the population will join the fight against Qaddafi. However, it looks like we are heading down the path of ever increasing American involvement. We started with a no-fly zone, then started hitting ground forces, and now the CIA is actively involved. This would seem to put us on the path to a real war (declared or not) against Libya. After all, until Qaddafi is deposed or the rebels give up, we will be stuck in the situation (unless we are willing to leave the rebels to be slaughtered).