If that were true than the could be no possible world (=a world that can be described without contradiction) in which God did not exist. But it seems obvious that there can be such a world. Consider this description:
World W = a world in which only a single pencil exists.
It's hard to spot the contradiction in that simple world!
But it's not at all difficult to see that a possible world containing only a pencil is contradictory. When we are talking about possible worlds we are not saying, "Imagine a universe with only a pencil in it at a given point in time." But a possible world in which only a single pencil exists is a possible world in which a pencil exists without anything -- past, present, future, material, immaterial -- to cause it. To say that a world can exist in which only a pencil exists is to say that it is possible for a pencil to exist as a brute fact with no further explanation. But pencils are composed artifacts; as such they are effects, and thus World W is a world in which an effect exists without its cause. That's a contradiction. The only way one can get around this is to argue that pencils can, in fact, be brute facts, i.e., things that are not caused by anything at all, don't necessarily exist, and yet can still happen to exist for no reason whatsoever. But this stretches the concept of a pencil beyond all recognition. Moreover (although full consideration of the question would require a longer argument than this), it is a contradiction for something to exist uncaused and not be necessary, since what exists but is uncaused is something that exists whose existence is not contingent on anything else.
And it's easy to see that the matter is not going to be as easy as Smith suggests, because if God is a necessary part of the explanation for why anything other than God could exist, God is necessary. But it's easy enough to see that this will be a common reason for saying that God is necessary; and therefore no one can be sure of the coherence of the claim that a possible world in which nothing exists but a single nondivine entity unless they are already sure that God is not necessary for the explanation of the existence of any nondivine entity. In other words, the World W argument boils down to the claim, "Well, it just seems obvious that it's possible for God not to exist; just think of what it would be like for God not to exist." But this is just question-begging from the beginning.