I'm as big a fan of Germany and European democracy as the next man. But Roman democracy was hardly the same thing as modern democracy.
*cough* Greek democracy came first...
And the Romans weren't that different, really. You were a citizen, you got a vote. And their tribus system for voting (you vote in your district, then the district gives one collective vote) is no different from the current US system. The only real difference I can see is that voting rights weren't universal, but when you think that Switzerland didn't allow women to vote until well into the 1970s, that's not that "unmodern" either. Personal wealth as a factor of how much your vote counts for was still around in the 1900s too.
The constitution worked as well for them. They had the mos maiorum, and enough of a legal system that laws were well published, could be changed and abolished. In the late republic, legal representation was available too, and while bribes were involved, it also worked along the principles of proof. There's a reason why Roman Law is the basis of European legal systems. They had the senate to function as a parliament, the consuls, praetors etc. as the elected government, and the tribunes of the plebs as the checks and balance system who could even call all citizens in to vote for major issues.
The Romans actually had a very modern approach to elections, too. You could buy votes, bribe other candidates, lobby your way into getting the support of parts of the elite, spread rumours, marry a woman of an influential family... and if it all didn't help, you claimed a god told you it was okay. You tell me where that's different from what happens in modern democracies.