Frankly, when they ask Jesus (I think it is in Luke): Are there not six days in which to heal? – I always thought that was a pretty good question. Unless you look at it from the point of view that Jesus’ time was short to accomplish his work, and he was constantly being pressed by hordes of people clamoring to be healed. He was packing in as much as he could do. Many places in the Gospel describe scenes not unlike the rush to get Elvis away from crowds who were clawing at his clothes (and body), so the pressure was on. Jesus had a healing power nobody else could deliver, and in mercy “delivered” as much as he could in the time allotted.
Also (still thinking like a Christian), in John, again, Jesus, healing on the Sabbath, is challenged and replies “My Father is working still i.e., always], and I am working.” Now (remember: thinking like a Christian) if Jesus is the Son of God, and does what the Father does, he can without guilt heal on the Sabbath because the Father heals on the Sabbath.
I understand the Rabbis of that time used to say that God was always working, holding the world in existence, and that if He should stop, the whole enterprise would disintegrate. So “working” on the Sabbath kind of fits in that context.
Jesus also states that “The Sabbath is made for man, not man for the Sabbath.” In another place, he really packs a wallop by stating that “The Son of Man is Lord of the Sabbath.”
We Christians, I think, really have no IDEA what an inflammatory statement that must have been to the guardians of the law.