As I recall, the system was set up with 3 branches of government in tension. Obviously, that was naive.
That was hundreds of years ago; when Madison says "domestic faction", he doesn't mean "a faction", he means what we would today call "factionalism". The 18th-century use is a pretty direct mirror of the Latin word factio, also meaning factionalism.
The idea that "checks and balances" are built into the US governmental structure is interesting. It would make sense if governmental positions were held by right of heredity. They aren't, but you can see how the Framers would be working with that mental model.
As the US government is actually constructed, Congressmen, for example, have no incentives to preserve anything as a power exclusive to Congress, because they have no lasting affiliation with Congress.