The Roman Republic was in a death spiral and would have ended regardless of the civil war. It was a matter of 'when', not 'if'. The Republic was in tatters by the Late period and beset my multiple problems which ultimately doomed it.

One of the major triggers was caused by Rome's success on the battlefield. Her armies were in the Republican period nothing more than a citizen militia. Originally when they were fighting in Italy it wasn't an issue, since the campaigns were brief (one summer) and the men would be back in the fall to work their farms. But as the campaigns took the men farther and farther from Italy, they were spending longer and longer away from their farms. Soon the armies were fighting in Spain or North Africa for years. Soldier's farms began to fail in their long absence and without their property they lost their qualification for the militia. There's also suspicion that the frequent pace of service combined with the declining numbers meant some men were being called to duty again and again. This may have led some to avoid the census and thus no longer appear on the militia rolls. All this meant a steadily decreasing pool of men who were eligible to be called up for service - at a time when the Romans were fighting constant wars in their far-flung territories. Eventually one general (Marius) waived the property requirements and accepted volunteers (some suggest he was not the first to do so).

These new volunteers came from the abundant landless poor who were attracted in the hope of a land grant following the successful completion of the war. Unlike the previous conscripted militia, they had no farms to return to. These men were wholly reliant on their general as only he would have the political muscle to get that done. This would change the nature of the armies and their relation to their commander. Soon the armies would become private armies of clients fighting for their patron's interest. Without this, there would be no armies ready to march in support of the civil wars.

Another watershed was the addition of political violence. The Gracchi were both murdered and their killers never punished (under the fig leaf that they aspired to seize power). From this point, violence entered into the political lexicon and would be seen with political gangs fighting bloody street brawls and the burning of the senate house.

The ambitions of the elites themselves was another factor. There had always been competition between elites over the high offices but by the Late Republic the stakes had grown and things had been turned up to 11. The Republic had been designed to run a city-state but was now trying to run an empire with roughly the same amount of administration. Corruption allowed men to amass huge fortunes and this wealth was injected into politics with bribery becoming rampant. This in turn meant elections required massive amounts of cash forcing these elites to borrow heavily (they were land rich but lacked liquidity). Success in the electoral process meant eventually gaining governorship of a province which could be exploited to amass sufficient wealth to pay off his creditors (c.f. Cicero's description of Verres). However a loss meant political oblivion.

Political intransigence was another cause. Factionalism had hardened so greatly that compromise was no longer possible. As tensions mounted between Caesar and Pompey, the former made an offer of compromise that could have defused the situation. This was supported by the majority of the senate but the faction leaders of the Republicans shut down any discussion - Caesar was too much a threat to their political dominance and they were willing to set the Republic on fire to eliminate him. I put a lot of the blame on Cato the Younger since his decisions are a major reasons behind the death of the Republic. He worked to politically humiliate Pompey following the general's successful return to Rome. This and other decisions created a coalition between two inveterate enemies (Pompey and Crassus). To defeat Cato's faction, the Triumvirs resorted to political violence (using Pompey's veterans) and the Catonians replied in kind. He then worked to pry Pompey away from Caesar and align him against the proconsul in Gaul. When Caesar made various offers to try to defuse the situation (as noted previously), Cato and his faction shut down any discussion.

But ultimately the person who ultimately lit the fuse on the on the fall of the Republic was Sulla. He was ambitious (and they all were ambitious) but had the skills to back it up. He was the first to march with his army to topple the state (controlled by a rival faction). After the civil war, he had his surviving opponents murdered and then went about rewriting the rules to 'fix' the Republic. Then he retired as the most powerful and renowned man. This created the precedence - you could seize power, murder your opponents, rewrite the rules, and then retire.

So what was Caesar up to? Ultimately we don't know since he was killed. Maybe he ultimately would have followed Sulla's example and eventually retired, maybe he would have he held onto power.