In joining Ms. Rice and Ms. Power, Mrs. Clinton made an unusual break with Secretary of Defense Robert M. Gates, who, along with the national security adviser, Thomas E. Donilon, and the counterterrorism chief, John O. Brennan, had urged caution. Libya was not vital to American national security interests, the men argued, and Mr. Brennan worried that the Libyan rebels remained largely unknown to American officials, and could have ties to Al Qaeda.
The bottom line is that this is now the State Department's war, and the Defense Department is reluctantly following Obama's orders.
And note, that in his public addresses about the war, Obama uses weasel words to avoid stating that HE ordered the attacks.
See also THIS: