Absolutely. Republican sentiment continued long after the death of Caesar. It wouldn't been too difficult to argue that it never really went away either. As far as Roman elites of the time go here are a few of the things we know: Augustus Caesar made great efforts to ensure that the forms and functions of the Senate remained symbolically intact. He insisted on not being called king, dictator, or any of the other titles his adoptive father flirted with- this was in many ways key. Indeed the success of Roman empires can often be measured in how they balanced their own power with concessions to both the senate and the plebeians. The skill with which this balancing act was done was considerable and many emperors notably did not possess them. Individuals such as Caligula and Nero who may have been loved by the people but ignored symbolic concessions to the senate and flaunted imperial power were the victims to assassination plots. Anthony Everitt's biography on Augustus is a great source of information concerning Augustus. Suetonius provides some further insight in that it often names plots, or attempted plots against the emperor(s): invariably accusations of republicanism followed these plots. Although there was an early purge of leading republicans and anyone who opposed Augustus, republican forms and ideals remained. The ideas of men such as Cato and Cicero continued to be revered.