Jenny's number "Kaput" is a direct reference to Mein Herr from Cabaret, specifically Liza Minelli's performance. The song and the choreography are almost exactly the same.
The girl who dies--Jenny's roommate--is named Elsie. This is a direct reference to the song "Cabaret"--the relevant lyrics are: "I used to have a girlfriend known as Elsie / With whom I shared four sordid rooms in Chelsea / She wasn't what you'd call a blushing flower... / As a matter of fact, she rented by the hour! / The day she died the neighbors came to snicker: / 'Well, that's what comes from too much pills and liquor!' / But when I saw her laid out like a Queen / She was the happiest corpse I'd ever seen."
The opening "Welcome to Schmicago" uses the opening tune to Pippin, "Magic to Do" which introduces the audience into the carnival, similar to the song's purpose here.
In the hotel lobby, the drunk woman shouts "I'll drink to that!" echoing a famous lyric from Ladies Who Lunch from Company by Stephen Sondheim.
Does that shock you is taken from Big Spender, from Charity, with heavy references towards Cabaret.