You can probably guess the title of this post is meant in a tongue-in-cheek way. John Calvin lived 1,500 years after the earthly ministry of Christ! Besides, Calvin's responsibility was to fall in line with Christ's teachings, not vice-versa! So no, Jesus wasn't a Calvinist. But Christ's teachings in John chapter 6 shed light on the issues of sinful inability, election, faith as a gift, and the eternal security of the believer.
Christ criticized the crowd for chasing after Him for wonder-bread (6:26), showing their reasoning was off. He exhorts them not to work for perishable food, but to work for the food that endures to eternal life, which He will give them (27). Christ's word shoots down an ancient hyper-Calvinist error, that only the elect should be evangelistically exhorted. Christ exhorted that whole crowd without any exceptions. He tells all of them to believe in Him.
"What works are those?", asks the crowd (28). "The work God wants is for you to believe in Me, whom God has sent," Christ replies (29). The crowd asks about works, plural. Jesus replies with one work, singular: believe. We are saved by one work, faith in the Gospel, not by the many and varied fruits of that faith in the life.
The crowd, in what has to be seen as a defiant, unbelieving response (considering they already saw a mighty miracle), demand more bread miracles from Jesus. (30-31). Jesus brushes aside their demand, and changes the subject. For one thing, Moses didn't work the manna miracle. For another thing, God was offering them the heavenly bread right there at that moment (6:32). That "bread" was Jesus Himself, who came down from heaven and whose mission was to offer life to the world (32b-33). "Give" here means "offer", which shows that God can offer a gift but still have it rejected.
The crowd asks for this heavenly bread (34). Christ says, "I am the heavenly bread. If you believe in Me, you will never hunger or thirst spiritually again!" (35). But the crowd had seen Him, teaching and working miracles, and they still hadn't put their faith in Him (36). Miracles in themselves do not convert. There is something in the proud, stubborn souls of men that defy even the most obvious evidences of Christ.
The entire crowd had seen Him, and the entire crowd had not believed. But Christ said there was another, smaller group who do come to Him and believe: people God had given (37).
In fact, Christ said that everyone in that group, without exception, comes to him. So here we see two kinds of giving:. God at that moment was giving (offering) Christ to the crowd. But God at some time in the past had given some people to Christ. Christ will for noever reject those people, because His mission was to do the Father's will (37-38). It was the Father's will that Christ accept them.
God's will is also that none of the given should ever be lost, and all of them shall be raised up at the last day (39). This verse tells us that it is impossible for them to ever lose their faith; and it is impossible for any of them to ever go to hell. This group sees (understands) Christ and trusts in Him, and receive assurance of everlasting life (40).
The Jewish leaders get riled at Christ over Christ's claim of pre-existence (41-42), but Christ rebukes them (43). He's the Messiah, so of course He was pre-existent.
Christ then says that only the people God draws can believe in Him ; no one else has that ability (6:44). If God leaves someone alone in the tar-pit of their own ignorance, they can't pull themselves up out of it in their own strength.
Christ also says that anyone the Father draws will be raised, which appears to say they all come to faith (He did say that earlier in v.37). This is consistent with Isaiah 54:13, in which all of God's true disciples are taught by the Lord. If God spiritually speaks-to and teaches someone, that person comes to Christ (45). Apparently God can be mighty persuasive.
Christ hastened to add He didn't mean that people have a direct vision of God (46).
The sole condition for eternal life is belief in Christ (47). Christ himself is the bread of life (48). The manna didn't give everlasting life, but Christ does (50-51). His "bread" is His body, which he would sacrifice on the cross on behalf of the world (51).
Notice that the historical cross is the place of His one-time giving of His body, not at communion.
The Jewish leaders griped even louder at this (52). Jesus doubles down on the symbolism: you need to eat His flesh and drink His blood, otherwise you remain spiritually dead (53). His body and blood are the real food of God (55). Anyone who eats His flesh and drinks His blood lives in Christ, and He lives in them (56-58).
Now, many of His disciples recoil (60). Christ asks if this teaching offended them (61). How would they react if they saw Him go back to heaven? Would that upset them, too? (62) Christ makes it clear that His physical flesh would profit them nothing. He isn't talking about literal bread, any more than He was a literal sheep-door or a literal vine. Eternal life comes from the Holy Spirit, working through Christ's words (63).
Christ interprets their revulsion at His teaching as an evidence of their true unbelief (64). Just because someone called himself a disciple of Christ didn't make it so.
Christ hits them with a hammer blow: None of them can savingly trust in Christ unless God grants that they shall (65). Christ said this earlier to the crowd, but now He says it to His own disciples. A man could follow Christ around, sit in His Bible classes, even be baptized, but that doesn't mean he has spiritual power to believe in Christ. The spiritual power to believe in Christ comes from God alone.
As a result of Him saying this, many of His disciples abandoned Him (66), proving that they were secretly unbelievers the whole time.
Christ asks the twelve disciples, "Do you want to leave, too?" (67) Peter professes that Jesus is the Christ, the Son of the living God, and that He alone has the words of everlasting life (68-69). However, Christ reminds them that one of them was a child of the devil (70-71).
So, was Christ a "Calvinist"? Or, to put it more seriously: