I really love Roman history. I'm just a hobbyist here (i.e. I've read a ton of biographies on great Roman leaders), so please correct me if any of my thoughts here are incorrect.
My feeling has been that Sulla's purges were the effective end of the Republic. Rome had no bureaucracy. It instead relied on great administrators (like Pompey, for example) to carry out public work projects effectively. The conflicts of the 80s not only thinned out talent from entering into the oligarchy, it required the entry of new men or men with families with less auctoritas like Cicero and Caesar. The emergence of new men created a rift between the optimates (conservatives, traditional oligarchy) and new folks that reduced compromise and lateralized society further.
Cicero was very moderate most of his career until his attempts to split up the Caesarians after the assassination, even so he found himself butting heads with stubborns like Cato his entire life. Caesar felt as though his hand was forced in the civil war, as the optimates wanted to arrest him for his land reform a decade earlier as consul as soon as he put down his imperium from the Gallic campaigns.
I would perhaps argue that the largest parallel the US has with Republican Rome is the breakdown of compromise and trust alongside increased lateralization. One can examine vote pairing incidence in the US Senate to observe this: recently Lisa Murkowski voted "present" during the Kavanaugh vote to allow a republican colleague to go to his daughter's wedding. Vote pairing used to be commonplace, and is seen as a gesture of compromise and good will, but it is very, very rare nowadays.