The charge does not accuse Him of healing but of breaking Sabbath regulations. In both cases, Jesus repudiates the charge by arguing 1) that the works of salvation are contemplated by the Sabbath commandment (see Deuteronomy 5:15, where redemption is the focus of the keeping of the Sabbath), and 2) that what Jesus did—being contemplated by the Sabbath law—is equivalent to God doing the same thing. It was this that really angered the Jews because they surmised that He not only had "broken the Sabbath" but in their eyes did something far worse: blaspheming God by making Himself equal with God.
It ought to be obvious that Christ did not regard the Sabbath as a time of idleness. He certainly looked at it far differently than the Jews did. He admitted that what He was doing here could be considered as work.
But what kind of work is it? Since He equated Himself with God, what He was saying is that He was doing the work of God. That is His justification. "My Father is working until now," and He did not break the Sabbath!
It is interesting that the word "answered" in verse 17 also appears in verse 19. It is the only place in the New Testament where this particular Greek word is translated "answered." It is a particularly strong word. What it means is that Jesus was heatedly defending Himself. It is showing that He considered their accusation to be "personal," as it were, and He reacts to it very strongly.
What comes out of His mouth is, "My Father has been working till now, and He works on the Sabbath!"
Then Jesus answered and said to them, "Most assuredly, I say to you, the Son can do nothing of Himself, but what He sees the Father do." (John 5:19)
Jesus is saying, "I am imitating what I have seen My Father do. Therefore, I am not breaking the Sabbath because God does this on the Sabbath!"
What we have to figure out is what kind of work does God do on the Sabbath? This is important to understanding the principle of the kind of work that is permitted on the Sabbath. What does God do that Jesus is copying?
God shows that He rested from His work. The kind of work that God is doing on the Sabbath does not involve the work of physically creating something. So we can eliminate that right away. Notice John 1:1-3:
In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made [past tense] through Him, and without Him nothing was made that was made.
John is referring to the physical Creation. Those works were finished, as it were, from the foundation of the world. Jesus is not referring here to the work of earning a living. The work that God is involved in is something else entirely!
God does His work ceaselessly and effortlessly. Jesus is telling us what kind of work it is: the work of redeeming. It is the work of salvation. It is the work of healing people, particularly their minds.
In John 5:31-36, Jesus Christ says, in essence, "What I am doing proves that I am the Messiah." At that time, He had just healed someone, redeemed him from bondage to an illness, from uselessness. He just gave to him the liberty to have hope. He just delivered someone out of his discouragement. That kind of work is the work of salvation. God "is working salvation" (Psalm 74:12).
Also consider John 6:29: "Jesus answered and said to them, 'This is the work of God, that you believe in Him whom He sent.'" God is working to produce in us faith in Jesus Christ because salvation is by grace through faith. Faith is the foundation from which everything in God's purpose grows. God is working to get us saved. He is able to do it, but we have a part in this salvation in that we have to make choices. The basis of our choices is whether or not we believe in Jesus Christ. If we believe Him, then we will make the right choices. It is essential, then, that our faith be increased.
So, the purpose of the manifestation of the works of God in Christ is to produce faith. If one has faith in God, then what will he do? He will apply God's Word, and that produces liberty in himself and in others. We can now begin to see the part that the Sabbath plays in this. It is essential to increasing our faith.
The work that God is doing is not the work of a physical creation but the work of a spiritual creation. He is creating sons in His image. Christ is Redeemer, Deliverer, Savior—and that is His work! What does He spend His time doing? He spends His time healing, forgiving sin, teaching the way of God, and doing good. That is His part in the work of God.