Gaius Julius Cesar delivered the coup de grace to the Republic by demonstrating it was possible to completely dominate Roman politics through military might and personal popularity. The Senatorial faction killed him and kicked off another round of Civil Wars.
Gaius Octavius, who would style himself Caesar Augustus after his posthumous adoption by Gaius Julius Ceasar managed to out bastard everyone else to gain control of Rome. He made a show of restoring the Senate, publicly according them their old privileges, but creating what would come to be called the principate, a collection of powers that had formerly existed in the Republic, but without any limits, and which, when used together gave him effective control of the government. Chief amongst those was control of the military.
Tiberius Caesar Augustus inherited these powers position from Caesar Augustus; and depending on your source, either quickly degenerated into tyranny and perversion, or was slandered by subsequent historians. Either way, he didn't screw things up badly enough to cause a revolt, despite being the original doomer (Seriously, he was called "tristissimus hominum" or "the gloomiest of men" by Pliny). And between the 37 year reign of Augustus and the 23 year reign of Tiberius, the system had been in place as long as most people had been alive.
Nobody in the Senatorial class really liked Tiberius. Even if you take the most charitable view of him, and ignore the rumors of kiddy fiddling as smears, he was hard to get along with. Tiberius in turn, persecuted enemies in the Senatorial class, real or imagined.