If Syria's modern anti-ship weapons are operational then we are going to lose a warship or two. If they are not operational then expect Russian force to hit anti-Assad forces in retaliation for our strike(s).
(Of course ground to air just might take out our missiles in which case the administration is just embarrassed and not much more happens)
Next step would be for Iran and Syria to launch an attack on Israel. Both claim they intend to do exactly that so maybe they will. What then? Will Israel simply "take it" or will Israel respond? Should Israel respond then Russian will be forced to respond to that and us to defend Israel and there you have it folks WW3 is on once Russia hits US forces in the med or Turkey.
So the questions are, can Syria hit our ships? Can Iran hit Israel? What assets does Russia have in the region? Does Russia think Obama will back down if he is starring nuclear war in the face? China may want in on the action too, but I think it more likely they will play it smart and sit this one out.
China, for one, is interested in Asia and in Africa. Is trhe US a paper tiger? Does the US panic when a single ship is sunk? The Chinese will definitely take note of how we behave. And the Iranian nuclear program, and North Korea, and others.
Global Power is in flux. The WWI analogy has been done to death, but there is good reason to think that great nations will make some bad choices and then it will all go smash.