Here are my opening two cents on the complicated situation in Libya:
Value and limits of US power: The US cannot and should not try to impose its will on the world unilaterally. It doesn't need to do so really. Many countries benefit enormously from a world organized in the way the US likes it to be organized. The US should not need to always be the unilateral "international cop." Sometimes direct US involvement simply isn't worth much of a US commitment even if the stakes are high for some of our allies. I think that is the situation in Libya. The stakes are much higher for Europe than they are for us and it is as correct as it is novel that Europeans shoulder the majority of the burden here. But even if the US doesn't want commit much, the US is unique in its ability to project power around the world. The Western European militaries are very capable. They have air forces that are nearly as capable as ours. They operate fancy jet fighters like F-16s, the Rafale and the Eurofighter/Typhoon. These forces are more than a match for the aging and poorly trained Libyan air force. But they will be hard pressed to operate those air forces even in nearby Libya. The Europeans will probably need US logistics support if not US combat support. A friend of mine in the USAF told me that even if they are operating from bases in Sicily, F-16s (for example) would probably need to refuel on the way to and on the way back from Libya to give them much air time over the combat area.
Why the Situation in Libya Matters More to Europe than to the US: If there is a bloodbath in Libya, it would provoke a massive refugee crisis in Tunisia and Egypt both of which are in no position to deal with such. Very quickly, many of those refugees would end up in Western Europe (especially France, Italy and Spain). Also, there is the possibility that European leaders still feel some shame about their inability to act in Bosnia in time to prevent a bloodbath there. While Americans may look at Libya and see Iraq: Part II, Europeans see besieged Libyan towns like Misrata and Benghazi and fear another Srebrenica. At the same time, the current President of France, Sarkozy, is facing Bush-like disapproval ratings. Two thirds of Frenchmen disapprove of his policies. Sarkozy may be trying to "wag the dog." Much of that disapproval is tied to Sarkozy's reaction to the revolutions in North Africa and the Middle East (his initial move was to stand by Tunisia's ousted dictator - le oops).
What the US Should Do: I think Obama is correct that this is NOT a situation that warrants the commitment of US ground troops. The only exception to that I could imagine being worth while would be a temporary deployment to secure a landing zone to evacuate a small number of foreign nationals or perpetrate a snatch and grab operation to kidnap/arrest Gaddafi and get the heck out of Dodge. I don't think anything that happens in Libya (even the emergence of an Islamist regime or the shut off of Libyan oil) is worth the long term deployment of US troops.
What Will Happen Next?: The short answer is: "who knows?" It's up to Gaddafi, who is probably lurching from one psychotic break to another, and the people around him. All of the inner circle people in Libya probably fear, with much justification, that there are few options for them other than to go out in a blaze of gunfire. If the US has visions of a decade of quagmire in Iraq and the Europeans have visions of Srebrenica, Gaddafi probably has nightmares of Saddam Hussein's execution and the killing of his sons in gun fights. If he would have thought more clearly, he would have jumped on a plane to Venezuela as soon as things looked to get ugly. But the man is clearly insane. If you make me guess, I'd put my money on Gaddafi trying to go down fighting. So far it looks like Gaddafi is trying to retake as much of the country as he can before European forces can get into action. There are rumors that Egypt is arming the rebels in Benghazi. If that's true, there may be a scenario whereby France, Spain and the UK et al, cripple Gaddafi's forces with air strikes which gives the rebels time to get organized and equipped to take over the country themselves. It's worth noting that every time the Libyan army (based on the Islamic Legion and its successor organizations) has gone up against organized resistance they have been routed.