Francis Fukuyama mentions this in one his books -- The Origins of Political Order or Political Order and Political Decay, I can't remember which -- and argues that this is an important part of how American democracy was workable (and British democracy too, by the way).
Other thinkers with related ideas are mentioned by other commenters:
As far as I can remember, Fukuyama's idea was that small organizations gave people a way come together as members of a certain community of practice or interest -- a trade, religion, a hobby -- and to gain first hand experience with self-governance. The organizations also provided a way give the shared concerns of their members a public voice. It's not feasible for a political candidate to visit every tradesman of every stripe in his shop, but when the horseshoers have a regular meeting at their hall, a candidate can often arrange to visit the hall for an hour or two. The same is true for ladies' charitable societies, religious groups, libraries, map collectors and many other groups that represent certain interests or powers in the society. These organizations were often (though not always) chapters in larger organizations, which provided a way to really focus people's voice at higher levels of government.
I believe the absence of these social organizations is more or less the cause of the imbalance in US democracy today. It simply is not workable for the individual to face off, toe-to-toe and unmediated, with the state.
It would be remiss to overlook the role of the church in 19th century American society. There was something of a religious revival. And the nature of a single congregation is that it never grew past the limits of a small, personable organization. While there was a flourishing of denominations, there was nothing akin to outright sectarian conflict or violence. So there was this small, personable network of congregations in intimate contact with each other that spread throughout the entire country, with small nodes every few miles or so at least.
"There is nothing, according to me, that deserves more to attract our regard than the intellectual and moral associations of America....
In democratic countries the science of association is the mother science; the progress of all the others depends on the progress of that one."
[0] https://press.uchicago.edu/Misc/Chicago/805328.html