The first thing to note is that there were believers who were part of the Sanhedrin: Nicodemus (John 3:1, 4, 9; John 7:50; John 19:39) and Joseph of Arimathea (Matthew 27:57, Mark 15:43, Luke 23:50, John 19:38). That is two out of 71 members of the Sanhedrin. We have no idea whether others could have been converted after Jesus’ resurrection. Further, Acts does note priests becoming Christians (Acts 6:7). So there were those in positions of leadership who did become Christians. But I think it is safe to assume that the majority did not. So why not?
A large part of the ruling class was made up of Sadducees. The Sadducees as a sect of Judaism did not believe in the resurrection, spirits, or angels. Since they had wealth and power, they were primarily concerned about the maintenance of the status quo. So I think their reasons for rejecting Jesus were largely political. They didn’t want anyone upsetting things with the Roman Empire. They wanted to continue in their positions of prominence. Pride and possessions got in their way.
For the Pharisees and the rest of Judaism, politics also plays a part in the rejection of Jesus. It is just the politically opposite side from the Sadducees. This side wanted revolution and ultimately got it. They wanted to kick the Romans out and have Israel be in charge of Israel. This would lead to the First Jewish-Roman War (AD 66-73), which included the destruction of Jerusalem in AD 70, and the Bar Kochba Revolt (about AD 132-136). Jesus was offering them a kingdom, but not the kind of kingdom they wanted. I think this played a significant part in the rejection of Jesus.
We must also consider Paul’s statements in Romans 10 and 11. Paul writes: “For I bear them witness that they have a zeal for God, but not according to knowledge. For, being ignorant of the righteousness of God, and seeking to establish their own, they did not submit to God’s righteousness.” (Romans 10:2–3 ESV) Ignorance of scripture and spiritual pride played a part.
Paul reminds his readers that a “remnant” out of Judaism did in fact respond to the gospel and were saved (Romans 11:5), but Paul does note a hardening:
What then? Israel failed to obtain what it was seeking. The elect obtained it, but the rest were hardened, as it is written, “God gave them a spirit of stupor, eyes that would not see and ears that would not hear, down to this very day.” (Romans 11:7–8, ESV)
The question then is how does hardening work, whether in the case of Pharaoh in Exodus or the Jews of the first century? I take as a given: “God shows no partiality” (Acts 10:34). People are morally responsible for hardening their own heart. Yet, there is some sense in which God hardens hearts. I think it is in the fact that God presents us with his saving acts and a choice. The condition of our heart determines whether we will respond favorably to God or reject God. As the saying goes, the same sun hardens clay and melts wax.
They are very human tendencies: materialism, ignorance of scripture, and spiritual pride. God and his saving acts in history present all of us with a choice.