This 1936 pop song plays at the start of the scene between Sookie and Jackson, and was written by Sammy Cahn, Saul Chaplin, and L.E. Freeman. The version used on the show is by Dean Martin, and is from his 1960 album This Time I’m Swingin’!
The lyrics to the song say, “If that isn’t love, it will have to do/Until the real thing comes along”. It seems to be a comment on Lorelai’s relationship with Max.
The Annotated Gilmore Girls 