"...but when once they were told that democracy was established, they shut their eyes and went to sleep."

GKC quote found via the American Chesterton Society's Facebook page:
Men kept an eye on despotism and they kept an eye on aristocracy; but when once they were told that democracy was established, they shut their eyes and went to sleep.

UPDATE 04-18-17

The quote is taken from the essay "The Old Vigilance, published in the New York American, September 30, 1933, and republished in the July/August 2011 issue of Gilbert Magazine