The last day in question is the day of the resurrection of the believers, of the just and unjust.
See John 5:
24 “Truly, truly, I say to you, he who hears My word, and ( W ) believes Him who sent Me, has eternal life, and ( X ) does not come into judgment, but has ( Y ) passed out of death into life.
Two Resurrections
25 Truly, truly, I say to you, ( Z ) an hour is coming and now is, when ( AA ) the dead will hear the voice of the Son of God, and those who ( AB ) hear will live. 26 For just as the Father has life in Himself, even so He ( AC ) gave to the Son also to have life in Himself; 27 and He gave Him authority to ( AD ) execute judgment, because He is the Son of Man. 28 Do not marvel at this; for ( AE ) an hour is coming, in which ( AF ) all who are in the tombs will hear His voice, 29 and will come forth; ( AG ) those who did the good deeds to a resurrection of life, those who committed the evil deeds to a resurrection of judgment.
Then we have in John 6:
35 Jesus said to them, “ (AV) I am the bread of life; he who comes to Me will not hunger, and he who believes in Me (AW) will never thirst. 36 But (AX) I said to you that you have seen Me, and yet do not believe. 37 (AY) All that the Father gives Me will come to Me, and the one who comes to Me I will certainly not cast out. 38 For (AZ) I have come down from heaven, (BA) not to do My own will, but (BB) the will of Him who (BC) sent Me. 39 This is the will of Him who sent Me, that of (BD) all that He has given Me I (BE) lose nothing, but (BF) raise it up on the last day. 40 For this is the will of My Father, that everyone who (BG) beholds the Son and (BH) believes in Him will have eternal life, and I Myself will (BI) raise him up on the last day.”
Words to the Jews
41 (BJ) Therefore the Jews were grumbling about Him, because He said, “I am the bread that (BK) came down out of heaven.” 42 They were saying, “ (BL) Is not this Jesus, the son of Joseph, whose father and mother (BM) we know? How does He now say, ‘ (BN) I have come down out of heaven’ ?” 43 Jesus answered and said to them, “Do not grumble among yourselves. 44 No one can come to Me unless the Father who sent Me (BO) draws him; and I will (BP) raise him up on the last day. 45 It is written (BQ) in the prophets, ‘ (BR) And they shall all be (BS) taught of God .’ Everyone who has heard and learned from the Father, comes to Me. 46 (BT) Not that anyone has seen the Father, except the One who is from God; He has seen the Father. 47 Truly, truly, I say to you, he who believes (BU) has eternal life. 48 (BV) I am the bread of life. 49 (BW) Your fathers ate the manna in the wilderness, and they died. 50 This is the bread which (BX) comes down out of heaven, so that one may eat of it and (BY) not die. 51 (BZ) I am the living bread that (CA) came down out of heaven; if anyone eats of this bread, (CB) he will live forever; and the bread also which I will give (CC) for the life of the world is (CD) My flesh.”
52 (CE) Then the Jews (CF) began to argue with one another, saying, “How can this man give us His flesh to eat?” 53 So Jesus said to them, “Truly, truly, I say to you, unless you eat the flesh of (CG) the Son of Man and drink His blood, you have no life in yourselves. 54 He who eats My flesh and drinks My blood has eternal life, and I will (CH) raise him up on the last day. 55 For My flesh is true food, and My blood is true drink. 56 He who eats My flesh and drinks My blood (CI) abides in Me, and I in him. 57 As the (CJ) living Father (CK) sent Me, and I live because of the Father, so he who eats Me, he also will live because of Me. 58 This is the bread which (CL) came down out of heaven; not as (CM) the fathers ate and died; he who eats this bread (CN) will live forever.”
The last day is the BODILY ressurection, hince the "raise up".