i don't think this is correct, but i hear it a lot. let me explain --
He says "pick up your cross" -- that's not equivalent to "crucify yourself"
Romans 6 tells us, we have been crucified with Him. done. completed. it commands us, "consider yourselves dead to sin and alive to God" through Christ, because we have already been crucified with Him. Colossians 3 tells us, we have died and presently our lives are hid in Christ -- this is something finished, completed, already having happened. the instruction to 'take up your cross' is to carry these facts with you, not to perform them all over again as though yesterday's baptism into Him was insufficient.
it is like the comparison the author of Hebrews makes, saying that under the law the priests had to keep making sacrifices over and over, adding more and more blood to the altar daily to cover sin. but Christ has died once and for all -- do to say 'crucify yourself' every day is like saying 'you were born again yesterday, now be born a 3rd time today, and be born again tomorrow -- be born again and again and again and again...'
either He has saved us or He hasn't; either we have died with Him or we have not. we are born of the Spirit or we haven't been. i don't think that by saying 'pick up your cross daily' it is meant, keep starting over from square one. but remember Him and what He has done. don't walk around, as James says, like a man who looks away the mirror and immediately forgets who he is. James isn't saying you have to go become that person again over and over; he's saying, as Paul says, 'be unleavened, as you really are' -- and we really are, or else what has Christ done for us? anything at all? if i'm having to repeat His work for Him every day it hardly makes sense to say that 'by one sacrifice He has perfected forever those who are being sanctified'
you maybe know the old saying, that if you're crucifying yourself you're gonna have a hard time with that last nail. it may be trite but there's a real truth to that: crucifixion is something that has to be done to you by someone else, and it generally doesn't need to be 'redone' once it's happened.