Actually, I believe it is far more pedestrian than that.
Crucifying by the Romans was a fairly common occurrence. It was a spectacle that made the locals understand that they ought not trifle with their Roman occupiers.
Before a person was actually crucified, they would be flogged and beaten, usually in the prison courtyard. Beaten so badly, in fact, that the condemned actually begged for death to come. The reason for this was the Romans did not want the locals to see a man struggling against the soldiers as they put him on a cross. They were concerned that this would make the condemned look heroic, fighting to the very end. This would not serve the purpose of the public crucifixion. Therefore, once the captain of the guard was satisfied that the condemned man had no fight left in him, he would command the condemned "take up your cross and follow me!" If the man refused, the flogging would continue until he did as he was told. He would then pick up the cross beam and carry it to the place of execution, knowing what awaited him if he changed his mind and decided to fight his executioners. He accepted his fate. He surrendered.
When Jesus said "Take up his cross and follow me" he was not referring to bearing a burden, but rather to complete surrender, complete denying of one's own will and desires to the will of God in their life. It means to put one's life in God's hands to do with it what He will. And the people understood because they knew what it meant when the captain of the guard commanded "Take up your cross and follow me!"