I use these terms because they are the language of political science, which would have been understood by the Founders in similar language and with similar concepts. The concepts came down from classical usage for the most part -- Plato, Aristotle, Polybius, and Cicero would have been familiar to the educated men among them, and likewise the dark musings of Tacitus on the subject of how tyranny grew up in a great republic, and how the morally and politically downfallen condition of his own countrymen contrasted bleakly with the vigor and virtue of the free Germans, whom he professed to admire. These lessons will absolutely not have been lost on the Framers, who were very conscious of the Aristotelian life-cycle of societies, and who were educated in the received vocabulary of political science.
Madison was famously concerned with faction, from his knowledge of the English parliamentary system and from Polybius, who particularly condemned the bad influence on Athenian policy of the demagogues. Of course, Pericles was a demagogue, too, but Polybius likes to overlook that when currying favor with his Roman masters by comparing them to Pericles and deprecating the Athenian model in favor of the Roman.
Madison believed very much as the Bush family do, that politics ought to be a hobby of the idle (but educated) rich. I don't agree with him all that much, except in this, that a republic dominated by combinations of schemers is a Bad Thing. I catalog Faction among the diseases of Republic (along with straight-ticket voting and The Lobby, among others). But I'm enough of a Jacksonian to think that the country was better off when ordinary men paid close attention to politics, and made strong demands on the ethics of their politicians. The memoir of Davy Crockett that someone posted to the Internet -- I think here on FR -- was a small classic, and the kind of thing I want to see more of, in which an honest farmer gave his congressman a stern lesson in ethics and showed him why he shouldn't have voted for a pork appropriation. Madison never contemplated such a scene: he was above correction by mere yeomen. So I take many of his lessons, but I reject his classism and country-squire comfort with the idea that "people like us" would run the country, and all the rest of us fall down with gratitude at their transactions on our behalf.
The larger nation allowed more free play for groups to combine and work for common goals.
But that's Faction!
It also allows greater stability as divisive issues, powerful interests and the political ambitions of politicians and their followings are diluted in the larger sea of national life. The result is more freedom for the individual from those who would dragoon him or her into this or that local army or party.
I don't know whether I agree. Sure, Boss Tweed and Joe Pendergast and corporate actors like the Central (Southern) Pacific Railroad in California and the Mellon Bank in Pennsylvania suborned and seduced people's officeholders to their own agenda. But now we see the same thing happening at the national level, and we hear of similar initiatives being transacted across national borders by conspiracies of corporations, NGO's, and semi-governmental groups from terrorist groups to transnational bureaucracies and secretariats.
One can already see a national consciousness developing then.
Well, sure -- among people who thought they were going to drive the train and ring the bell, and among people who wanted to. But saying so doesn't tell us whether a national consciousness is better than a local one. It is the prejudice of history that wider is better, but then historians are toadies to power who'd like to have been players themselves, so I think we should regard their point of view as treacherous, and not a good indicator of where the best interests of the people lie, but only the enthusiasms of students of Machiavelli.
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.