A common line in dramas, this cannot be taken literally because everything is a situation. The implication is that we have a bad situation.
This phrase is used as understatement, meant to be said in a way that is not alarming, "loaded" (with panic), or more specific as to the type of situation (accident, incident, crisis). The idea is to instantly get the full and serious attention of the listener while remaining as calm as possible.
Example: "Mr. President, we have a situation. An airplane has been hijacked." The listener is not being bombarded with details (yet) because there is a certain protocol to follow; a President would ask for details about the situation, but that is his choice and his privilege. You do not shout down the President.
This type of line could easily appear in a movie, a television drama, or a novel. It is certainly not limited to presidents, but has been made famous in that context in American English.