I have lived in the US for my whole life, and there definitely is an Exceptionalist doctrine, particularly among the Republican party. However, the ideas of American Exceptionalism and Manifest Destiny go back much farther than WWII, all the way to the Puritan ideas of "civilizing" Native Americans to "Fifty-Four Forty or Fight!" to Roosevelt's imperialism and on. It's so ingrained in our national history that it's barely even questioned (any surprise why there has never truly been a viable Socialist movement in America?).

Your point about immigrants is interesting, though I'm not really in a position to comment on it. I can tell you, though, that a good portion of the US is very hostile to immigrants, and we have had a history of hostility (take a look at the Chinese Exclusion Act, for an extreme example). Our current political discourse is also very anti-immigrant, too, and the path to citizenship is very lengthy and difficult.