I'd be a bit less definitive : Roman elites were certainly much opposed to an hellenistic-like kingship in Rome, both for ideological reasons as well than for political ones, and had forces to show their discontent efficiently.
Monarchism was seen at this time, nevertheless, (even if it blossomed only later, blostered by the new wave of civil wars), as a modern and relativly popular ideal, critically among stoicians : the idea was that a man, raised and full of virtuous ideas could topple a gathering of corrupt or not so virtuous man. Basically a charismatic regime.
It was less important than it was during first emperors' reign (and it's clear that not only the population didn't mind the principate, but generally it was more democratic than the late republic) but the idea was already there and the huge reaction against the plotters points that Romans weren't epidermically opposed to a charismatical regime, quite at the contrary.
Be careful then to not confuse the reaction of Roman senatorial elites, and the deep tendencies : I could see Caesar amorcing slowly a change towards what we knew being the classical patriciate of Julio-Claudians, towards a more monarchical/charismatical Roman Republic, while being extremely cautious when it would come to the less "Roman" aspects.
He seems indeed to have avoided the title of "Rex", but it may have been avoided for Romans mostly as with the preparation of a campaign against Parthians, he could have assumed functions of an hellenistic king in order to gather around him (and interestingly, that could have been a real problem with Romans : as for Marc Antony, a too great collusion with oriental despots would have been cakewalk for his opposers to discredit him)
Don't take Romans for more formal than they were : opposed to a "Rex" they would have been opposed to someone having the same powers but as "Dux" or "Imperator". (Heck, if "Rex" was anti-nomic with the Roman Republic, so was "Dictator for life"). Already at this time, toughts about how personal power could be preferable to the rule of elites over the people were blossoming and title would have little mattered either for the people than for the Senate.