Actually, the best explanation I have heard for Jesus's exclamation on the Cross is referential. If I were to say to you, "Four score and seven years ago", you would understand I was talking about The Gettysburg Address.
Here is the opening of Psalm 22: "My God, my God, why have You forsaken me?". I would argue that Jesus is pointing those around Him to this Psalm (known as the Suffering Servant Psalm) to help them understand what they are witnessing. Although it begins in agony, the Psalm ends in triumph.
I thought that when Jesus cried out "My God, My God, why hast Thou forsaken me", was when God turned his back on Christ because Christ had taken on the sins of the world and God will not condone sin.
Interesting. I never realized that.