The question of what res publica means is a thorny one, and one which I do not intend nor think I am able to tackle within the confines of reddit. Nor, I want to make it clear, am I necessarily disagreeing with Kaldellis' argument. I do not know enough about it to do so categorically. There are certain elements of what has been suggested here and elsewhere on this thread that are incomplete, however, and could use a little revisiting. For example:

In the final decades of the Republic a tribune with a gang of a few thousand street thugs who could clear the streets of opposition would effectively control the voting electorate, and thus state policy. See Milo, T Annius and Pulcher, P Clodius.

Neither Milo nor Publius Clodius did so. Cicero's rhetoric makes it seem that way, but if the actual incidents of violence mentioned in Cicero and our other sources are cataloged the picture presented appears very different. Only on a relatively small handful of occasions did Clodius' muster turn up in full, and only once was a comitiate election ever disrupted. Clodius' supporters, who probably did not even number in their most violent core so many as a few thousand, held great influence over the (senatorially-controlled) courts and were able to prevent individual opponents like Pompey from interfering with Clodius' legislation for a very short time. They had very little influence in the electorate, although Plutarch makes an interesting, if so vague as almost to become meaningless, comment that Clodius organized the urban plebs εἰς τὸ πολίτευμα, "for politics" (i.e. probably the vote). While it's true that the demographics of the Republican elections were troublesome, this:

they didn't all hike over to Rome for every election or assembly. They just weren't in a position to do so

is emphatically untrue. Indeed, Publius Clodius is the first tribune to rely on the urban plebs as a main base of support. Previous tribunes, beginning with Ti. Gracchus at the latest, had always relied almost exclusively on rural support, and introduced urban measures as minor affairs that kept the urban plebs satisfied enough not to interfere. So the Gracchi (both of whom were killed when their rural supporters, who had previously entered the city in great numbers in support, were prevented by the harvest from leaving their plots), Saturninus, Sulpicius Rufus, probably the younger Drusus, and Catiline (not a tribune but still very relevant). What precisely changed under Clodius is not entirely clear, but until the 50s relying on the urban plebs was simply not a productive tactic for an aspiring tribune. In the centuriate assembly the urban plebs were in the main capite censi or at best in the middling property classes--easily outvoted by even small-time rural landholders of the sort that dominated the Italian population. In the tribal assembly there were only four urban tribes, and the thirty-one rural tribes ranged against them could and did easily overpower them consistently. Precisely who was entering the city during elections is not always especially clear--surely the more affluent landholders could travel more easily than small-time farmers, although Mouritsen has shown that pretty much the same thing can be said of the urban poor, for different reasons--but come they most certainly did. There is no shortage of attestation of rural migration during elections.

All this is to say that some of the underlying questions are not at all resolved. If the basis of our current line of reasoning is the degree of democratization in the Republic vis-a-vis the later Empire then we must have a reasonably good understanding of the democratization of the Republic. But we don't. Maybe thirty or forty years ago we thought we did, but all that's been pretty much discarded and we've found we really don't know what to make of the democratic process of the Republic. So many parts of it are contradictory, and in emphasizing one part we often find ourselves neglecting something else. What are we to make, after all, of the claims made by Clodius and his successors (for an entire generation of tribunes sought to repossess Clodius' image, for reasons not entirely clear to us) to the exercise of tribunician authority? Is the total shutdown of senatorial power, by tribunician veto, plebiscite (initially not legal), or extralegal violence not essentially the purpose of the office of tribune, to protect the plebs' right to democratic voice? Would its appearance not be an indication of some very real social movement as much as any individual taking advantage of an urban electorate so totally unconcerned with politics as to be strung along at the whim of their leaders (a suggestion no longer taken seriously, at least not as I've described it)? We don't know, at least not definitively.