During the early Republic, especially its first generation who personally witnessed the tyranny of Tarquinius Superbus, Romans were very sceptical of the dual consuls who, for all practical matters, had the same power as the kings. Instead of limiting their power in the creation of the magisterial office, the idea was limiting the time they would wield said authority to one year. The second consul who ruled alongside Brutus, Collatinus, was actually exiled for his relation to Tarquinius.

The Middle Republican period saw the continued resentment of anyone fancying themself a monarch. Every dictator during this period resigned after the crisis they had been called upon for had passed, indicating that they would be torn to pieces if they tried to cling to power. Although it seems that Plebeians were allowed to hold the office of consul from the very beginning, it wasn't until the fourth century BC that one of them had to be a Pleb.

During the late Republic, the Senate, newly empowered by Sulla, passed into true oligarchy as the historical venues of popular reform (Principally the Tribunate) were stripped of their power and prestige. Since legal advancement was no longer an option, more and more ambitious minded senators broke away to back the landless poor in order to further their careers. The Republic had badly needed reforms for land distribution but also for the role governors play in their respective provinces. Governorships were in reality a way for senators to make themselves rich off the backs of the provincial tax payers and it only became scandalous in the Senate if their leeching became egregiously exploitative.

The early Imperium is usually labelled as the Principate, and the Emperor was known as the Princeps, or First Citizen. This was a result of Augustus' manoeuvring within the bounds of the Republican system in order to create the façade of continued democratic rule. His control of all affairs would be masked by only influencing through his immense wealth and control of the legions. The consuls were still elected every year and the Emperor himself, even the terrible ones like Nero, could be held in very high esteem by the urban masses if he threw enough games and was liberal enough with the public dole.

During the late Imperium, the style shifted from Principate to Dominate out of circumstance since the Republican façade's usefulness had been drawn out. In an effort to establish some semblance of legitimacy after decades of economic and military disaster during the third century Diocletian took to styling himself as Jupiter with his co emperor, Maximian, being affiliated with Hercules. He wasn't stark raving mad like Elagabalus though and he most likely didn't actually think he was a god, it was just a useful tool to make the Emperors seem less approachable from, let's say, potential assassins. In practice, this would mean that he would wear a diadem and make anyone who approached him have to supplicate themselves by kneeling before him and addressing him as your lord and master.

I hope I established that Romans would have radically different views of politicians depending on their location and the time they lived, so if you have more questions I won't hesitate to elaborate on anything else you want to know more about.