Does that crisis in some way create a new legal regime, a change both in international law and in American constitutional norms?
I think it's pretty clear that an American attack, without the sanction of the United Nations, the support of allies, the authorization of Congress -- or, it must be said, much hope of meaningful success -- would violate the Constitution. As Jack Goldsmith writes in Lawfare, it "will push presidential war power beyond where it has gone before."
Since the very beginning of the Republic, presidents have used force to defend American ships, military personnel, and civilians abroad. No one doubts, in 2013, that a commander-in-chief could order emergency military action to defend Americans, or the nation as a whole, from attack. And sometimes that emergency power has been stretched to include a real-time response to fast-moving events that threaten world order, even if U.S. targets are not involved. Time enough, when seconds count, to consult Congress after the dust has cleared a bit.
American presidents have also used force, without consulting Congress, to fulfill American treaty obligations. The most famous example was President Harry Truman's decision to commit American troops to the war in Korea without requesting authorization even after the fact. Truman argued that he was obliged, under the U.N. Charter and a Security Council resolution, to come to the aid of South Korea, and that that obligation superseded Art. I § 8 cl. 11's reservation of the power to "declare war" to Congress alone.
President George H.W. Bush, in seeking authorization for the first Gulf War, claimed that he did not need it, because of a Security Council resolution authorizing action against Kuwait. (The bluff worked, and Congress approved the war.) President Bill Clinton committed U.S. forces to intervention in the former Yugoslavia, and never sought authorization. In Kosovo, there was no Security Council resolution, but Clinton claimed to be acting under the NATO Treaty and at the request of the other nations of the Balkans.
How do these precedents apply to Syria? Not well. First, the crisis is undoubtedly an emergency -- but it is not an emergency that demands presidential action within minutes or hours. The U.S. is preparing in deliberate, even stately, fashion for a carefully choreographed attack on Syria; there's plenty of time for the president to invoke the "extraordinary occasions" language of Article II § 3 and convene a special session of Congress.
Internationally, a strike against Syria would go well beyond the flimsy justification offered even for Kosovo. The Security Council has not authorized action against Syria, and will not. Even with U.N. personnel producing the evidence that the Damascus regime has used chemical weapons, the U.S. apparently does not plan even to ask for permission to use force. The nations in the Middle East region have not asked for U.S. intervention. NATO does not support it -- and for heaven's sake, not even Britain will stand with the U.S.