Well, if you were up 40 hours straight FOR work, which I suspect is the case, then you had every right to fall asleep on your desk at work. Maybe that will clue your bosses in to the ridiculousness of the situation.
They need to hire more staff if they want to get stuff done fast. Human productivity can't last through 40 hours and more of work.
Honestly, what I've read of your job just sickens me.