So am I correct in understanding that there are two questions here, which do not necessarily overlap at all? The question of the "democratic" Republic and the question of the perceived destabilization of the Republican state? If not I recommend you think of these as two separate questions, because if you're going into this assuming they're linked you're setting yourself up for bad methodology. These are sort of the singlemost central questions of the Republican historian, so to be perfectly honest the reading list even to begin to answer them is...every classical text ever written dealing with the late Republic. Certainly all the important ones: Cicero, Caesar, Sallust, Suetonius, Plutarch, Cassius Dio, Appian, Velleius Paterculus. Writers like Aurelius Victor and roughly contemporary poets like Propertius or Catullus usually end up on department reading lists even for historians, simply because they preserve a lot of attitudes and incidents that are not necessarily in our "historical" texts. For stuff like "popular" opinions epigraphy becomes quite useful, but one must know how to use it. The question of the Republican "democracy" and the place of the plebs within it has become much-discussed since Brunt wrote The Roman Mob and openly challenged the concept of the "idle plebs." Importantly, Fergus Millar suggested that the Republic was truly democratic, an idea that hasn't received very much support. The most important work on the subject is certainly Mouritsen's Plebs and Politics in the Late Roman Republic, which is more or less the standard view now, namely that while on paper the Republic might have seemed highly democratic in practice socially, economically, and even just spatially the ability of most individuals to participate in political action, even elections, was highly restricted. A good addition to this is Morstein-Marx's Mass Oratory and Political Power in the Late Roman Republic. The similarity in titles I think is no accident, and Mass Oratory expands on and shores up a lot of stuff in Mouritsen. On the subject of late Republican "destabilization" even more has been written. Syme in the Roman Revolution argued that collapse of the Roman state was inevitable, which Meier picked up again later: if Caesar had not come along someone else would have. Gelzer (and to some extent Shackleton Bailey in his commentaries) pushed against this, noting the highly adaptive power of the Republican state. If you can read German I can think of few more digestible summaries of much of the debate here than Ungern-Sternberg's article Die Legitimitätskrise der römischen Republik, which as the title suggests interprets the political struggles of the late Republic quite plausibly as a crisis of political legitimacy