The exact wording of the "Americans can always be counted on to do the right thing…" quote varies a little bit from time to time, but it essentially conveys the same message -- Americans are a self-interested people, but they eventually do the right thing. But did Churchill ever say this, or even something like it? No. At least he never said it publicly, and there's certainly no evidence that he ever said it privately. Like dozens and dozens of other political quotes, they get attached to Churchill somehow. It's as if he's standing on a busy street corner and passers-by keep slapping unattributed quote bumper stickers on him until he rivals Shakespeare and the Bible for the world quote record.
Professor Buzzkill History Podcast