All the President can do is throw his support behind the amendment and use the bully pulpit to persuade Congress to take up the matter. Constitutionally, the amendment process is solely within the purview of the U.S. Congress and the many states. The President has no legitimate vested authority in the matter beyond that of being a citizen. Yes and somehow we are almost lead to believe that he has the ability to stop gay marriage. But I suspect it is his enemies that want us to believe that so that we will be mad and take our votes elsewhere if he doesn't. We wind up shooting ourselves in the foot.
You believe correctly.