Absolutely! Keep in mind that Octavian's wars were the final cycle of a struggle that had been going on for a century, and which spared not a single element of Roman society. Now, granted, the designation "Republic" and "Empire" are somewhat artificial and a bit misleading--when speaking of specific periods of Roman politics, classicists don't use those terms. To call the Roman state prior to Augustus the Republic doesn't really mean a whole lot. Republic comes from Res Publica, which is just the Latin way of saying government (any government, although monarchies are usually referred to by a different name). The Republic changed quite a lot over the several centuries of its existence, and this was something that the Romans were keenly aware of. Even so, the century of the civil wars was seen by most informed observers as a breakdown of civil morality and justice in the face of a mad dash for power.

Much of the way we think of Augustus' early days is the result of Victorian scholars buying Augustus' supporters' writings on his public works and justice and so forth. Augustus was a wily guy, and he wasn't about to make the same mistake his great-uncle Caesar had made. That is, Augustus was going to make damn sure that he disguised the legality of his supreme power (even if everyone was well aware that he actually was the guy pulling all the strings) so that no one could challenge him on a legal or even a moral basis. It was for this reason that Augustus went to such great lengths to emphasize that the Senate and the magistrates were returning to power after the anarchy of the civil wars, not because he actually wanted to restore the Republic. The Victorians loved the idea of Augustus as the Benevolent Tyrant, as they called him, and wrote a lot about how great he was--so much that it's still difficult to stop thinking about him like that, even when Syme smashed that view of Augustus back in the 30s.

What the Romans thought of Augustus should never be based on what the Victorians say, since they ignored everything in the textual corpus that didn't support what Augustus himself said. The first thing that should be noted is that the Late Republic was a period of unparalleled social commentary and free speech that afterward was never equaled. The civil wars were very obviously a period of turmoil for people. What seems to be glossed over in history courses these days is just how traumatic it was for Italy. High school and college history courses like to talk about periods of pinpoint action, like the various marches on Rome, or Caesar's war against Pompey in the east. This often leads to the misconception that most of the fighting was done abroad, particularly in the east and in Africa. While this is true for Caesar (it's often said by classicists that the best moral decision Pompey ever did was to leave Italy) it's far from true as a whole. Sulla and Marius devastated Italy with civil war, proscriptions, and the Social War. Octavian was originally enlisted by Cicero to annihilate the Caesarians seeking refuge in northern Italy, and when he joined Antony Italy had to face their proscriptions (which were far larger than Sulla's--a fact that Octavian liked to hide), plus Sextus Pompey's rampant piracy and coastal raids. Under Octavian Etruria was devastated during the war of Perusia, and southern Italy suffered heavily in conflicts with Sextus Pompey and the War of Brundisium.

Ok, so I mentioned social commentary and observation, right? Prior to Octavian's arrival on the scene we have observers like Cicero, Caesar, Sallust, Catullus (who shows just how conflicted people were in deciding who to fight for), etc. But we're interested in Octavian here. Horace, Virgil, Cicero, Livy, Pollio--the list of commentators on Octavian goes on and on. Unlike many earlier writers, who were often of the social elite and wrote mainly about Caesar's struggles with Pompey (which were mainly political or overseas, unlike those of Sulla/Marius and the Triumvirates--there's only one Triumvirate, the First Triumvirate is a fabrication of Octavian's and Antony's propaganda to legitimize their illegal pact by providing a precedent--which were all-out brutality), these observers were deeply wrapped up in this nonsense, often severely victimized by it. Horace fought on the wrong side at Philippi and owed Octavian his life, Virgil had his home seized and destroyed during Octavian's rampage through northern Italy and his proscriptions, Cicero was Antony's bette noire and was murdered on his orders, Pollio served as one of Caesar's best generals and his decision not to intervene on either side (due probably to his disgust at both the Caesarians and the Republicans) was one of the deciding factors for Octavian's early successes. None of these men were particularly fond of Augustus, but like much of Roman society they owed him a great deal, if only for ending the civil wars which otherwise would've surely torn the Roman state to pieces and irreparably destroyed Italy.

So, specific examples? Well, here's the thing. Most literary works after Octavian came to power were patronized either by him or his buddy Maecenas. Certain...themes...had to show up to gain approval. But it's selling these authors far short to say that they're merely propaganda pieces for Augustus--in fact, most of them criticize and attack Augustus more than they praise him. I wrote a writeup here dealing with Virgil's rather complex view of Augustus that is extremely relevant to this discussion and which I strongly urge you to take a look at to understand what I mean here. Livy opened his history by stating that the morals of Roman men have declined and are unrecognizable compared to those of their forebears, and quite often during his work he makes veiled jabs at Augustus (in fact, the last few books of his history seem to have been extremely critical of Caesar for destroying Roman freedom, which caused them to be hated by Augustus). Pollio seems to have respected Caesar, but despised Augustus--most of the material in Appian and Plutarch that is critical of Augustus and Caesar comes from Pollio's lost history. It's a bit ironic that Pollio, the Caesarian who hoped for the restoration of the Republic, was responsible for Virgil's favor with Augustus, when Maecenas noticed Virgil during a reading of a passage of the Aeneid that Pollio was hosting. Some of Horace's most emotional odes deal with his feelings about the Roman state and Roman society, how the civil wars have torn it to bits and he could do nothing to save it. Many of Horace's most famous poems are thinly-veiled attacks on Augustus, including his famous Ode I.37, in which he rejoices for Octavian's defeat of Cleopatra but at the same time praises her for her courage and steadfast mind (probably in parody of Octavian's accusations that Cleopatra was an amoral eastern temptress intending to furtively conquer Rome with her treachery) and implicitly suggests through his language that Octavian was unnecessarily cruel to her as a vehicle for his own rise to power.

Short version? Yes, Romans were well aware of what was going on. The intense social observations throughout the civil wars is one of the things that makes the Late Republic so fascinating