They threw outrageous parties
They paid heavily/heavenly bills
refers to the amount of money the couple are spending on their lavish lifestyle. The doctor reference doesn't occur until the last verse:
Call the doctor, I think I'm gonna crash
Well the doctor says he's coming
But you gotta pay in cash
which isn't necessarily a literal description of a crash scene with a literal payment (at a crash, not a house) but a continuation of the fast lane metaphor.