Obama's war violates the UN Charter, a treaty the United States has ratified, making it part of U.S. law under the Supremacy Clause of the U.S. Constitution. Obama's war also violates the War Powers Resolution, which permits the president to introduce U.S. Armed Forces into hostilities or imminent hostilities only in three situations.
Either the president needs some new faces in the Office of Legal Counsel, or his team needs to do what many of his allies on Capitol Hill are calling for: Ask Congress to grant new statutory authority for the military campaign against ISIL in both Iraq and Syria. What is the administration afraid of?
Whatever one thinks of the President's actions so far, it does not seem likely that there will be a majority in Congress in the near future to force the withdrawal of U.S. military forces. But there might well be a majority in the near future to insist that a military campaign that goes on for months needs explicit Congressional authorization.