How was the term 'The Cross' understood by the audience of Jesus? (Catholic perspective) At Luke  9:23 we read :

"And He said to all, “If any man would come after me, let him deny himself and take up his cross daily and follow me."

We also read at  Galatians 16:14  

"But far be it from me to glory except in the cross of our Lord Jesus Christ, by which the world has been crucified to me, and I to the world."

The concept surrounding the Cross, as we have today, was evidently  developed post-Resurrection. But the audience of Jesus, for whom Cross symbolized capital punishment awarded to criminals ( like what gallows symbolizes for today's generation), might have understood the term Cross  in an entirely different perspective. One would therefore surmise that either :(i) the usage of the word 'cross' was very much prevalent in everyday language of the people of Jesus' time , or, in the alternative : (ii) Jesus might in fact, have used some other term(s)  which the Evangelists later summarized in 'the Cross'  which had by then become a commonly accepted term. 

My question is: has the Catholic Church ever studied the prospects of option (ii) above ?
John 6:60 New International Version


  On hearing it, many of his disciples said, "This is a hard teaching. Who can accept it?"


Matthew 13:


  10 The disciples came to him and asked, “Why do you speak to the people in parables?”
  11 He replied, “Because the knowledge of the secrets of the kingdom of heaven has been given to you, but not to them. 


We don't know for sure, but Jesus had a reputation for speaking "hard sayings" and parables.    The Cross was a well known method of both execution and torture.   It was usually given to rebels and other notorious criminals.   So I propose that the disciples might have understood it in a literal fashion.   That following Christ might lead them to an end where they would share that fate, or in a more metaphorical sense that people who followed him would have to face suffering of various kinds.