That's a good question. I'm not sure about that.
I think overall it was largely a political decision in Washington that they didn't want to be seen to be out front, ahead of everyone else, on another intervention in that part of the world. There are also issues with President Obama's relationship with Congress, and about whether this was or was not a conflict that triggered a bunch of congressional involvements.
So there was a desire, definitely, to take a bit of back seat. I think that even applied before NATO assumed command. When Operation Odyssey Dawn was launched with the United States, Britain, and France, even then you saw President Sarkozy taking surely a more publicly prominent role in leading the charge, even before it transitioned to NATO leadership.