That's a good question.
The U.S. was initially reluctant to do anything in Libya. Secretary of Defense Robert Gates said famously at the time that for the U.S. to involve itself in another Muslim country, it would have to have its head examined, so he was opposed. Secretary Clinton was in favour of involvement.
The debate was very much an internal U.S. debate. Eventually it went to the U.S. President, and participation in the mission was decided on the basis of a number of criteria. One of them was a UN Security Council resolution that set out very clearly the nature of the mission, which basically was the protection of civilians, but also the U.S. decided at that time that it would not lead the Libya air campaign. The U.S. decided it would provide logistical support, surveillance, air-to-air refuelling, but that it would not provide any of the strike capability.