Gallup surveyed popular opinion in North Africa and the Near East on the Libyan intervention, and this is what they found:

Favor or oppose NATO in Libya

Some supporters of military intervention in Libya insisted that taking the side of the rebels in the Libyan conflict would earn the U.S. goodwill throughout the region. The image of the U.S. would change, we were told, because there was a groundswell of popular support for Western military action. Unlike Iraq, the Libyan war would not reinforce America’s reputation as a meddling foreign power, because Western intervention was supposedly what the publics throughout the region wanted. Like many of the other far-fetched claims made to justify and defend intervention in Libya, this one was wrong, as previous surveys have already suggested. Even in Tunisia, whose people might have the most reason to be supportive, opponents of the intervention outnumber supporters.

Among Libya’s immediate neighbors, a majority of respondents opposed foreign intervention in Libya’s conflict. When the U.S. and its allies invoked “regional” support for the war, it was significant that the Arab governments most in favor of the war did not include any of Libya’s neighbors. The “regional” support for launching a destabilizing war in North Africa was strongest among those countries that were not in North Africa and wouldn’t have to worry about any of the unintended consequences of the war. In fact, the governments of the countries neighboring Libya either wanted no part of the intervention or opposed it outright. It’s too bad that Gallup didn’t (or couldn’t) survey public opinion in Mali, but since the country is still being roiled by political disorder, military conflict, and armed separatism thanks to the Libyan intervention it likely would have been difficult to do.