Ruff brings up a couple of important points.
There is the obvious one of negligence. Through sleep deprivation, it is inevitable that errors in patient care will be made. The law firm of Dewey, Screwum and Howe will have a field day with you in court.
Secondly, yeah, how professional will your appearance be if you've been working 48hrs straight? If you don't have time to sleep, then you won't have time to shower either.