Lots of discussion--"this isn't who we are" or "this is exactly who we are".
The idea of "imagined communities" is relevant. People imagine what America is, they develop an image of who we are which is based on stereotypes and narratives from the media, schools, movies and TV, etc. So when a big event happens, it can be inconsistent with the image. That's not necessarily the case however. For example if we looked at the reactions shortly after 9/11 or the Boston marathon bombing I'd guess most people thought the reaction to the events was very "American" or "Boston" ("Boston strong").
Over the long run I suppose the image is sustained if the positive events outweigh the negative events.