What does the phrase "pick up the phone at 3 a.m." mean?

Question

I have heard the politicians and analysts refer to this numerous times during this election season when they say things like "who do you want to pick up the phone at 3 a.m.?" Does this particular time have a special meaning? Where did it come from?

Answer 1

Bill told Monica to do this.

the rest is history! :)

Answer 2

  This is from a Hillary ad.  It means to be ready to handle a crisis when you are totally unprepared for it.  Like getting an emergency call at 3 a.m.  

Answer 3

It refers to a call to the president in the middle of the night when he has to make a critical decision,instantly, such as going to war.