This 1986 song by English rock band XTC is playing in the background during the opening segment while Rory and Lorelai get ready for school/work.
The song is from the band’s album Skylarking; it is their best known album and generally regarded as their greatest work. It was initially ignored in the UK, but managed to get to #90. In the US, it became a hit on college radio and reached #70. Today it is regarded as one of the best albums of the 1980s.
Earn Enough For Us was never released as a single, but is the first track on the second side. The song is about a man struggling in a demeaning job to support himself and his wife in a ramshackle house. Learning that he is about to become a father, he is proud, but also worried about how they will manage financially.
It’s a reminder of the years of struggle to support herself and Rory that Lorelai has been through. The album came out when Rory was two years old, just as Lorelai began living in Stars Hollow as a single mother and working as a maid. Maybe it was a song that helped her get through those difficult early years.