In a nation larger state different interest groups or parts of the population have to cooperate and work together. They come to realize that they can't have everything their own way and that it's not a zero-sum game. I would not call this faction. I'd think of it more as the beginnings of a party system. I don't think one can really get around such division and coalition building and have effective government in a democracy or representative republic.
Maybe when the "interest group" side of things prevails over the "parts of the population" side you do get faction. If all the industrialists were aligned against all the farmers or workers, on might be able to speak of faction. I'd still find this to be less common in larger units, than in smaller ones. Factions could also be created along regional lines, or around charismatic leaders.
I'm fuzzy on ancient history, but I'm thinking of the death of Socrates and the ferocity some ancient city states brought to civic virtue and the defense of the civic cults. You can see some of this ferocity in Sparta and Rome. The freedom of the ancient city was very different from modern freedom, or even from the freedom of the empires which replaced them. It relied much more on civic virtue and on the freedom of the community to maintain it's cult and culture than on the freedom of the individual from external constraint. The freedom of the ancient city meant a tumultuous and often violent civic life filled with alarms and crises, though the Roman Empire was hardly free of such troubles, at least for those at the top.
I think one could understand Madison as trying to cope with this problem, to weigh or reconcile two concepts of liberty. His federal solution has had many noticeable successes. Individuals are still quite free in their personal lives, and have great mobility and a wide sphere of activity. Those who are attached to local cultures and their autonomy may regret Madison's ideas and the Constitutional system, but there was a trade-off between the autonomous or sovereign, self-contained community and the free and mobile individual. What the 20th century made of the Constitution is another matter, though. It reimposed regulation and regimentation at the federal level.
Features of government don't appear in isolation. A University of Houston professor taught a distance-education course a couple of years ago in which, unusually, he surveyed the stresses of American social and political life as seen through the prism of Hollywood. The concept was, that Hollywood puts up on the screen the themes and preoccupations that are on people's minds, and while the representations aren't even wildly approximate to the precision of a modern survey or long-form Census, nevertheless for the period of interest they incorporate additional information about the period about social conventions, fashion, preoccupations, and taboos. (Imagine what would have happened if Michael Jackson's or Rob Lowe's scandals had surfaced during, say, the trial of Fatty Arbuckle.)
Regardless of the distortions and deliberate suppression of really controversial issues (what will 24th-century filmgoers make of Arlington Road, I wonder?), the course did demonstrate the reflection, in film, of themes of psychological tension caused by the regimentation by business of urban and industrial life at the end of the 19th century, and the simultaneous (but unrelated? -- I don't recall) epochal shift in thinking from literalism and composition of thoughts based on the parsed and printed word, to the kind of thinking based on images and impressions, which the lecturer referred to as the more modern and, for membership in our era rather than the "premodern" era, determinative. These two developments occurred about the same time but I don't recall whether they were supposed to be causally related. I bring them up more to refer to the change in the work environment and the social environment, as cities became chicken coops (which the New Urbanism is trying to replicate) and workers became flogged peons in many industries. My own great-grandfather, who had personally known Bill Hickock, ridden as a scout with Custer, and watched the frontier settled and closed, in his last years with the Southern Pacific R.R. (I have his conductor's watch, a gold-plated and engraved Illinois Bunn Special) in the 1920's was working at the Indianapolis station, 12 hours a day, 7 days a week.......that's an 84-hour workweek, boys and girls, for a septuagenarian!