The Jews viewed Jesus Christ as a heretic Jew. In addition, he was a revolutionary albeit a non-violent one, that they felt threatened not only Judaism itself, but the power structures that went along with it in Judea.
The Roman administrators also felt threatened, as Jesus was another (one of many) revolutionaries or dissidents that were inciting oppposition to Roman rule. They executed him no differently than others before and after him in Judea.
As Judea was a particularly difficult province to govern, the Romans wanted the Jewish elite on side, and thus had a two-fold reason to deal with Jesus.
I think Sadducce (they only believed in the Tora) crucified Jesus because of his belief in Resurrection , even the Bible gives us hints to that. Honestly I highly doubt that the Pharisees played a a important role in the crucification of Jesus because they believed in resurrection like Jesus.
Acts 4 Peter and John Before the Sanhedrin
1The priests and the captain of the temple guard and the Sadducees came up to Peter and John while they were speaking to the people. 2They were greatly disturbed because the apostles were teaching the people and proclaiming in Jesus the resurrection of the dead. 3They seized Peter and John, and because it was evening, they put them in jail until the next day. 4But many who heard the message believed, and the number of men grew to about five thousand.
5The next day the rulers, elders and teachers of the law met in Jerusalem. 6Annas the high priest was there, and so were Caiaphas, John, Alexander and the other men of the high priest's family. 7They had Peter and John brought before them and began to question them: "By what power or what name did you do this?"