If Jesus had actually ever preached treason and/or sedition, the Pharisees would have had nothing to worry about: Neither Rome nor Herod took a lax, hands-off approach to protecting their authority & the history of Roman Judea is rich with incidents of incredibly brutal suppression of any hints of rebellion.
The Pharisees could sit on the sidelines as the Romans did their dirty work and tsk-tsk the process, secure in the knowledge that Roman persecution of political dissidents guaranteed they'd keep their profitable roles in the priesthood.
Nor was blasphemy a serious charge: This was first century Judea; the countryside was crawling with crackpot clergy and preposterous preachers. The Pharisees would have welcomed a marginalized would-be messiah with open arms, somebody who could shake things up without affecting any real change, somebody to debate against & denounce thunderously from the pulpit.
No, Jesus was no threat to them theologically.
Where the threat came was at the nexus of Roman rule and popular support. The Pharisees had been gouging the Jews for years, adding more & more increasingly complex & arcane levels of religious law that only became more & more expensive for the common folk to buy their way clear.
The common citizen of first century Judea had no great love for the Pharisees, and the Pharisees knew this, and the Romans knew this, and the Pharisees knew the Romans knew this.
So Jesus had to be eliminated as a threat to their monopoly of the office of High Priest. This meant destroying His value to the Romans. By raising a big stink over Jesus, by publicly accusing Him of treason and sedition, the Pharisees (more specifically, Annas' & Caiaphas’ clique) could guarantee no Roman governor would ever appoint Him as High Priest -- regardless of whether they actually executed Him or not.
So now the question becomes one of whether or not they really wanted him dead or, even if they did want him dead, did they really expect Pilate to grant their request?
Jesus alive was nowhere near as confrontational as his cousin, John the Baptist. Jesus didn’t have a history of seeking conflict with the Pharisees.
Oh, true, He railed against them on occasion, and famously cleared out the Temple of moneychangers, but almost always it was a case of the Pharisees confronting him, not the other way around.
John could really let ‘em have what for, but while they doubtlessly criticized him, there’s no evidence the Pharisees ever took steps against him.
That’s because John, for all his appeal as a firebrand prophet among the Jews, was not the sort of guy the Romans would have felt comfortable with. To them he was doubtlessly just another crazy Jewish prophet, and as long as he stayed in the desert & urged people to repent, they weren’t interested in him.
(In fact, John only got in trouble with Herod after he criticized the king for marrying his brother’s ex-wife, Herodias. This got him an express ticket to the dungeon, where he stayed until Herodias’ daughter, Salome, won his head as a door prize for pleasing Herod with her dancing.)
In a close reading of Scripture, Pilate comes off a lot better than the popular historical view of him. He repeatedly states Jesus is guilty of no crime, tries to fob Him off on Herod, tries to shame the Pharisees into turning Him loose by offering to release a despicable criminal in His place, tells the Pharisees to execute Him themselves if they’re so keen on it, and finally famously literally washes his hands of the matter.
Not a lazy, cavalier colonial bureaucrat but a competent, meticulous administrator who, nonetheless, gets hemmed in by Annas’ & Caiaphas’ clique, who were savvy enough to get the Romans to do their dirty work for them so they could escape any direct blame from Jesus’ fan base.
(Was this the carrot they dangled before Judas? A ghost of a hint of a whisper of a suggestion that maybe if he betrayed Jesus they could find a way of letting him into the inner circle and -- who knows -- maybe even the High Priesthood some day? The Gospel writers don’t know what transpired between Judas and the Pharisees other than he collected 30 pieces of silver -- not an inconsiderable sum in those days. Judas was the treasurer among the disciples, but one with sticky fingers. He may not have realized how much peril he was placing Jesus in & simply thought that his betrayal would just mean an end to His ministry & a chance for himself to make off with the bank account. If that is the case, it certainly explains his almost immediate remorse.)
So there, on the eve of Passover, Annas & Caiaphas & their clique get what they wanted: Jesus is not merely eliminated but his entire movement is now discredited in the eyes of Rome. Business is back to normal, the moneychangers are re-seated in the temple, the troublemaker gone, and the whole matter put to a satisfying end.
…or so they thought.