With thanks to CM:
“Pharisees are the legalists, the literalists. They, to a fault, tried to take every detail of the Law and make a burden out of it. They were the extremists.
Sadducees were the opposite kind, they were the modernists, the liberals. They did not believe in the resurrection, and did not believe in angels, and did not believe in the supernatural.”
With thanks to merriam-webster.com, “Definition of HERODIAN, a member of a political party of biblical times consisting of Jews who were apparently partisans of the Herodian house and together with the Pharisees opposed Jesus.”
First, which of the above would be the least likely to come to Christ and why. The Sadducees like many of today’s liberals did not believe in the resurrection of Jesus. Paul tells us in Romans 6:4-5, “4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life. 5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:” IMO, without a belief in the resurrection of Jesus there is no real coming to Christ.
Was King Herod even Jewish? According to answers.com, “King Herod's father was an Idumean and his mother was a Nabatean Arab. Herod was king of Judea because he conquered Judea by force, leading a Roman army. So, Herod was not ethnically a Jew and the Jews had every reason to resent his rule.”
King Harold seem to adhere to when in Rome do as the Romans do and when in Jerusalem be a token Jew. The Herodians not only oppose Jesus but were aligned with Rome. Coming to faith in Jesus would seem a remote possibility.
As the Pharisees were bound up in legalism they were very likely to have a thorough knowledge of prophecy. Of course 2000 years ago there was no Google so the information that Jesus was a Nazarene and born in Bethlehem would not have been as readily available to them. At least two members of the Sanhedrin came to faith prior to the crucifixion and resurrection, Nicodemus and Joseph of Arimathea. After the resurrection I would think there would be a crash course for the Pharisees who hadn’t earlier equated the activities of Jesus with the century-old prophecies . I would suggest that those of the Pharisees who could overcome the extreme guilt of knowing they facilitated the death of their Messiah would be convinced by the overwhelming evidence; that Jesus was indeed the long awaited Messiah.