This patriotic march by American composer John Philip Sousa plays while Miss Patty teaches baton twirling to a class of little girls. Sousa wrote The Stars and Stripes Forever in 1896, and it was first performed in 1897 to immediate enthusiasm. Generally considered Sousa’s masterwork, it is the official National March of the United States, and is usually played for the US President after he finishes a speech.
The Stars and Stripes Forever also has a special meaning in show business, especially the theatre and the circus, where it is known as “The Disaster March”. Traditionally it is used to signal that there is a life-threatening emergency so that staff can handle the audience’s exit without causing panic. One notable use of it in this context was at a circus fire in Hartford in 1944, where at least 160 people were killed.
It’s use in the show at this point may be meant to signify what a disaster of a day Lorelai is having.