I'm sure you don't mean this precisely. The Roman Republic was already long dead when the Caesars saved the Roman State by turning it into the Empire.
Corruption and intrigue among the ruling elites had destroyed any true republicanism at least a century earlier. Anyway, even at their best the Romans had a "Master Race" attitude which made the Nazis look self-effacing. We inherited their governmental mechanisms, not their ideals. Our ideals are descended much more from Christian principles than Roman ones. Roman and Christian principles were inherently antagonistic, as can be seen from the centuries-long attempt of the Empire to stamp out this subversive religion.