Elvis Presley gets the idea that he could do something for his country when he can work against society-undermining groups such as criminal organisations, drug dealers, communists and the like. In order to do that he wants to work as an undercover federal agent. He tries to set up a meeting with Nixon to arrange that.
The film indeed is about that very meeting, but much more about what lead to it. We see Elvis as a person with sometimes quirky ways of thinking, but oftentimes as an intelligent person. He tries to use his fame to get what he wants, but he is quite patient in his efforts. On the other side, two young people from the presidential staff try to arrange the meeting, but Nixon initially does not want to hear about it.
This results in an amusing film in which Michael Shannon plays Elvis and Kevin Spacey Nixon. Both do not look too much like the persons they play, but they perform their roles wonderfully.