Here is the thing though.
In Luke, every time he uses the word "today" - semeron in greek- it means TODAY:
Luk 2:11 For unto you is born this day in the city of David a Saviour, which is Christ the Lord.
Luk 4:21 And he began to say unto them, This day is this scripture fulfilled in your ears.
Luk 5:26 And they were all amazed, and they glorified God, and were filled with fear, saying , We have seen strange things to day.
Luk 12:28 If then God so clothe the grass, which is to day in the field, and to morrow is cast into the oven; how much more [will he clothe] you, O ye of little faith?
Luk 13:32 And he said unto them, Go ye , and tell that fox, Behold , I cast out devils, and I do cures to day and to morrow, and the third [day] I shall be perfected .
Luk 13:33 Nevertheless I must walk to day, and to morrow, and the [day] following : for it cannot be that a prophet perish out of Jerusalem.
Luk 19:5 And when Jesus came to the place, he looked up , and saw him, and said unto him, Zacchaeus, make haste , and come down ; for to day I must abide at thy house.
Luk 19:9 And Jesus said unto him, This day is salvation come to this house, forsomuch as he also is a son of Abraham.
Luk 22:34 And he said , I tell thee, Peter, the spammer shall not crow this day, before that thou shalt thrice deny that thou knowest me.
Luk 23:43 And Jesus said unto him, Verily I say unto thee, To day shalt thou be with me in paradise.
Luk 24:21 But we trusted that it had been he which should have redeemed Israel: and beside all this, to day is the third day since these things were done .
With the exceptions of Luke 12:28 and 13:32
That said, it is not 100% on either side of the argument.
Honestly, I think the only people that bother with these arguments are the people (like the JW's) that CREATE them to make themselves seem like that have "the real (tm) truth"

!
I re-state that, IMO, the point of that passage was NOT when but that he WAS Going.