The UN security council approved military action, specifically including the No Fly Zone. NATO was in agreement with the French very clearly in the lead on this one (they were first in). Given the adventurism we've subjected out allies to in other parts of the world it was going to be pretty hard for Obama not agree to at least a limited action and still call them allies.
and the US did most of the heavy lifting w/ respect to enforcing the "no-fly zone".
From there, the role was expanded to attack any support facilities that the Libyan government had; completely unrelated to flying.
Radar sites, C&C facilities; weapons storage facilites.
Everything that could be done without putting boots on the ground, the US did.
European equipment was unable to do the job; the US voluntarily stepped in to take over the workload.