This is expressly forbidden under pain of death in Jewish Law. Jews have a very strict code about certain things, that they are not to cause a Chillul HaShem, any situation that causes people to look upon G-d unfairly, and one of those is to give the impression that any Jew is being really nasty. If it was absolutely necessary, Jews might be required to act on their own to kill Jesus in secret.
This is one of the most implausible parts of Christianity. When you compare the teachings of Jesus to the Pharisees and Essenes then there's nothing new under the sun. Why would the Jewish leaders secretly gather in a conspiracy to get the Romans to execute Jesus (including getting witnesses to bear false witness against him) for teaching things that they themselves taught?
There is simply no connection between sin and slaying in the Passover tradition. Passover is the Jewish Festival of Independence. The eve of Passover is Jewish Independence Day.
My own theory is that the people who were inventing Christianity confused the Judas Goat with the Paschal Lamb. This would explain the odd story of Pilate releasing Jesus Barabbas and executing Jesus of Nazareth because of a tradition that the Jews supposedly had. Jesus N would have been the slaughtered goat and Jesus B would have been the goat driven from the town.