I might be able to answer this one! Well at least give insight. But I'm no historian and merely an enthusiast of Roman history. If my answer is not within guidelines, please mod let me know!

Short Answer: Most of the Roman people actually didn't mind or even cared. Continuous blood shed from civil wars and numerous political upheaval exhausted Rome's citizens and they just wanted stability.

Long Answer: The start of the fall of the Roman Republic and the rise of the Roman Empire arguably came from Lucius Cornelius Sulla. Sulla is considered to be one of Rome's greatest generals, having never been defeated in battle and even successfully attacked Rome.. twice! Sulla during the climax of his career (a little after 100 B.C. Note that Julius Caesar was a teenager around this point) had a dispute (understatement) with another well known Roman general, Gaius Marius. Long story short, Gaius Marius wanted command of the eastern armies that was legally given to Sulla by the Senate; Sulla gets backstabbed politically; Sulla becomes angry; Sulla uses his loyal Marius reformed army (ironically) to take back command and defeats Marius in battle.

Marius having been beaten, was exiled to Africa while Sulla finally returns his attention to the east. Though successful in his campaign, his absence allowed Marius to consolidate his power and returned to Rome. But again, in conclusion, Sulla attacks Rome a second time and becomes dictator. Sulla leaves his legacy for having set precedent of Caesar's march to Rome and to his dictatorship. Unlike Caesar, however, he actually gave up his power as dictator and retired to his villa until his death. Interesting man, that Sulla.

Anyway, that was the "First" and "Second" Civil War of that era.

Now in comes Julius Caesar. Julius Caesar, in 50 BC after having successfully subjugate Gaul, was ordered by Pompey to disband his army and return to Rome. Fearing that he'd be prosecuted after relinquishing his title as governor, he crossed the Rubicon river with his army and marched towards Rome causing yet again another Civil War. Caesar defeats Pompey and declares himself dictator. The senate wouldn't have any of that and so they decide to backstab him.. literally.

Another Civil War.

But this isn't about Antony and Octavian (Augustus) vs Brutus and Cassius just yet. This is actually Antony and Octavian duking it out before they formed the Second Triumvirate. Well they didn't go to war, but Octavian was recruiting Caesar's veteran soldiers to his side with some even defecting from Antony's forces. Antony did come to blows with the Roman Senate and was defeated in the Battle of Mutina.

What about Caesar's assassins? Well, Antony and Octavian (and Lepidus) finally reconciled and created the Second Triumvirate. With their combined forces, they went to war (Yep! Again!) against Brutus and Cassius (the leaders of the Liberators) and defeated them in the battles of Philippi. Julius Caesar was avenged and the Caesarian faction was the sole ruler of Rome.. Until everyone became power hungry.. again.

One more Civil War.

With Octavian ruling the West, Antony ruling the East, and Lepidus being an afterthought, Octavian and Antony co-ruled with a delicate alliance with one another. By 33 BC, despite Mark Antony being married to Octavian's sister, Octavia, Antony was having an affair with the Queen of Egypt, Cleopatra. Now this isn't much of a problem since it was just a political marriage and everyone and their mother cheated on their wife/husband, but after Antony's successful invasion of Armenia, he declared his and Cleopatra's son Alexander Helios the King of Armenia. In addition, he awarded the title of "Queen of Kings" to Cleopatra.

This was enough for Octavian to try to convince the Senate that Mark Antony was not looking at the best interest of Rome. And even more, Octavian found Mark Antony's will stating that his sons will inherit Roman conquered kingdoms and for Mark Antony's body to be buried in Alexandria. Now this is important because this was used as propaganda that Antony is no longer considering himself Roman.

The Roman Senate ended up declaring war on Cleopatra and Egypt. Mark Antony laid his loyalty to Egypt. In a similar fashion to Caesar's and Pompey's Civil War, Octavian (or really, Marcus Agrippa) defeats Mark Antony's Army in Greece and finally Antony and Cleopatra in Egypt, thus making Octavian the single ruler of Roman Republic.

Octavian, now known as Augustus, ruled while upholding republican traditions. He still gave the Senate power with acts like relinquishing his control of provinces and armies. But really, Augustus couldn't give up his authority for fear of another power struggle among generals. The "republic" was essentially Augustus' empire.

With Augustus however, over 100 years of political strife and civil wars had essentially ended. After 100 years of bloodshed and political instability, Augustus created an empire that achieved internal peace and prosperity known as the Pax Romana. So despite of them being proud of being a republic, peace is definitely better than endless war.

Source: Caesar by Adrian Goldsworthy; Augustus by Adrian Goldsworthy