Before NATO, there was a defense treaty between Britain, France, Belgium, the Netherlands, and Luxembourg. They wanted military aid from the U.S. to counter the U.S.S.R. and thus a new organization was born.
What if Harry Truman thought it would would be a bad idea to be tied to Europe since it would most likely be Europe that is in need of aid and not the U.S. so the alliance isn't made? Is the Warsaw Pact still made? Is the Cold War a lot more peaceful?
(It could still be called NATO if Canada signs the defense treaty.)