Glenn I said about the public support of the western people- Europe and Americas and also, specially, the support of the Arab League. They are important for europeans to be given a free hand to do whatever they think its more appropriate for them. Its a stronger support than the ones they needed to gather with the Iraq warII, since Ghadaffi is considered unpopular and crazy (Lockerbie issue, etc), and seems to be killing/attacking some of its own population, which gives free point for humanitarian intervention.
However the point is Ghadaffi past. Had he a clean past, it would be at least two times more difficult for western countries to declare the no-fly zone.
About the support of Lybian people, in fact, its important in the sense that you need to have some rebellians wanting change inside a country, and it doesnt matter if they are in a few number.
The opinion of the majority of the lybian people seems to be very irrelevant, I guess.
We are living still in a era where French Revolution and then American Constituion are very popular among western civilization, so every time a western country can sell the image of a crazy dictator that supress human rights of first generation, not being a great issue how he does that, its easy to get the support of the masses, right?