What does Stephen Vincent Benet hint is the cause of "The Great Burning" in "By the Waters of Babylon"?

The Great Burning was probably some kind of nuclear event because fire fell from the sky.

John’s society exists in a post-apocalyptic world.  There are many hints that it is our world, and the disaster was man-made.  For one thing, priests search the houses of the “gods” for metal, and the metal is dangerous to touch.  This seems to indicate that a nuclear event occurred.

The greatest hint that it was an atomic bomb or some other nuclear weapon that caused the destruction is the fact that John’s people remember the event, or at least seem to know what happened.

I saw both banks of the river—I saw that once there had been god-roads across it, though now they were broken and fallen like broken vines. Very great they were, and wonderful and broken—broken in the time of the Great Burning when the fire fell out of the sky. 

Fire might fall out of the sky if there was an atomic bomb. It could refer to the blast radius or to the acid rain that could follow.  Either way, it implies a serious event that eradicated large portions of the population, specifically in the city of New York.

In addition, nuclear blasts leave traces behind.  John seems to describe these when he says that there are “marks and stains” left behind from the incident.

It is not true what some of the tales say, that the ground there burns forever, for I have been there. Here and there were the marks and stains of the Great Burning, on the ruins, that is true. But they were old marks and old stains.

John also mentions “a mist that poisoned” and the fact that people were running around as the fire fell from the sky, and then their buildings collapsed.  Legends tell of the few who “escaped” and it is from them that John gets these stories.