Origins; as far as I know the term exists simply because the hand movement - with the help of a warped imagination - resembles shaking hands. The 'President' part comes about simply because, as many a male will tell you, the penis is the one making the decisions (for the man) in many female-male relationships.
1)Jeez, I wish I was at home shaking hands with the President right now.
2)Nah, I'm pretty bored. I think I might go and shake hands with the President.
3)Wow, there's photos in today's paper of your Dad shaking hands with the President!