Yes, I forgot that Luke's gospel says "daily". But actually the English adverb "daily" suggests that the taking up of the cross is to be done "day after day", or "on a regular basis." But, the Greek word is not the adverb "daily" but the noun "day" preceded by the preposition "according to", or "corresponding to", which is in the accusative case. As such, the translation "daily" is the translator's opinion on what Jesus meant to say when he used the accusative case with the noun "day".
While the accusative noun can be adverbial, the idea that one takes up his cross day after day is not literally true. A person can only die once. Or more to the point, he can only be executed once. And so the idea that Jesus wants us to allow ourselves to be executed as part of our day-to-day routine sounds very strange. In the context of Jesus statements that he was about to be captured and killed and after his rhetorical question about gaining a life but losing a soul, it seems really unlikely that he was asking his apostles to die daily.
The accusative, when associated with time, can also be translated, "at the time when." Now, I could be wrong but I think it is more likely that Jesus meant to say,
"The Son of Man must suffer many things and be rejected by the elders and chief priests and scribes, and be killed and be raised up on the third day." And He was saying to all, "If anyone wishes to come after Me, he must deny himself, and take up his cross [when his time comes] and follow Me."
Jesus is saying, "My cross is to bear the sins of the world and the time for that is now. Anyone who wants to be my disciple will need to bear his cross, whatever that will be, at the appropriate time."
Thanks. I agree. Goes perfectly with the contexts when Jesus used this terminology, which was doing whatever necessary to not deny him and preach the gospel. Could be forsaking houses or family, or could be death. One thing is certain, he was not talking about dying to self/soul-life/flesh/sin daily, which is what most use it for. Scripture is clear that has already been done by the cross of Christ.