I'd have to agree with SpaceRome, Caesar took advantage of the weaknesses of the first Republic and used them to break the institutions, but not the ideal, of the Republic. You have to remember the fine distinction between the mottos of the First and Second (and all subsequent) Republics.
1st - For The Senate and People of Rome
2nd - For The Senate of the Roman People
The rise of the Egalitarian Movement post Athens really did sow the seeds of the Second Republic, and is why the Athenian Senate was largely considered Father of Democracy whilst Rome is the Mother of Republicanism. Both traditions were vital in creating the precursor to the Federal Senatorial Republic we see today.
Vitally we saw the abolishment of Imperium, which isn't really understood today, but was effectively immunity from prosecution.