Final answer:
President Obama relied on his constitutional authority as commander in chief and existing congressional authorizations to conduct drone and missile strikes in Libya, without needing specific Congressional consent. The War Powers Resolution and similar historical precedents provided the framework for such unilateral military actions. This approach had been previously reinforced after 9/11 and used by past presidents.
Step-by-step explanation:
President Obama used a combination of constitutional authority, and existing congressional authorizations to use force to order drone and missile strikes against suspected terrorists in Libya without Congressional consent. He sent a letter to Congress arguing his role as commander in chief granted him the authority for such actions. Additionally, the War Powers Resolution allows the president to initiate military actions for sixty days without Congressional approval. The precedent for this kind of executive action had been set in various forms of authorization, including United Nations resolutions, NATO actions, and other international accords, which have enabled presidents since World War II to act without requesting formal declarations of war from Congress.
During the post-9/11 era, the Office of Legal Counsel to the U.S. Department of Justice asserted that the president could take necessary actions to protect Americans, further strengthening the president's hand in unilaterally ordering military initiatives. President Bush also exercised similar unilateral military powers, backed by Congressional authorization, in response to the terrorist attacks of September 11th, 2001.