What is the great river in "By the Waters of Babylon" by Stephen Vincent Benét?

The great river in the story "By the Waters of Babylon" is the Hudson River.  
The Hudson River is the river separating parts of New York from New Jersey. Most notably, the river separates Manhattan, New York from New Jersey. The great river, which John calls the "Ou-dis-sun," is one of the main clues in the story that alerts readers to which great city of the gods John is exploring.  

There was the great river below, like a giant in the sun. It is very long, very wide. It could eat all the streams we know and still be thirsty. Its name is Ou-dis-sun, the Sacred, the Long. No man of my tribe had seen it, not even my father, the priest. It was magic and I prayed.
Then I raised my eyes and looked south. It was there, the Place of the Gods.

The text quoted above is a major hint to readers that the story is not taking place in the past. The river name, when spoken aloud, sounds vaguely familiar (which is what Stephen Vincent Benét intended). The following paragraphs further cement the future setting by describing large "god-roads" that are broken and look line vines. That's probably exactly what an old and broken suspension bridge looks like, and Manhattan has a lot of suspension bridges leading into it.
As the story continues, details confirm "By the Waters of Babylon" takes place in Manhattan. Because readers know John is travelling east to the Place of the Gods, the great river that borders the Place of the Gods must be the Hudson River.