And the actual notes of "There's Bobby and Jackie and Jack" are not exactly the same as that recurring theme, but the intervals are similar. Only maybe slightly rearranged. ;-)
Also - there's a clear parallel (not musically, but in terms of the "story" of the songs) between "Who Wants To Live In New York" and Saturday Night's "What More Do I Need" - made doubly important when you consider that Sondheim has said that "Opening Doors" is truly autobiographical. Not that he's ever said that anything like the scene with Joe ever happened with "What More Do I Need" specifically, but since the song is from what was to be his first professional show, it's a fun connection.
One can perhaps also draw a connection between the downward scale that starts the title tune, and using the same figuration to start the verses to "Our Time." (That may be in Banfield actually, but I'm too lazy to go look it up lol.)