The disagreement with the Pharisees (If in fact there was one) was that a withered hand was not life threatening and it wouldn't have hurt the man to wait a day.
When Jesus pointed that a sheep (Matthew) or a son or bull (Luke) could be pulled from a pit or well on the Sabbath this was something that both sides already agreed upon. And this is not a violation of the Sabbath (For the thousandth time..)
The blood doctrine is far, far beyond anything even the Pharisees would have come up with.