Well, that's the rub, ain't it? The whole system that Madison and Adams and the others set up depends on the notion that everyone in the nation is generally on board with the idea that liberal democracy is good and should be protected. It never contemplated the possibility that a large percentage of the public would someday decide that it would be really great to be ruled by a strongman without regard to what the people want.
People want to be ruled by a strongmen
with regard to what the people want, that's exactly why they want a strongman. Same reason people went for Caesar - the governing apparatus of the Roman Republic was so sclerotic, corrupt, and dysfunctional that there was no way for popular sentiment to influence policy. That's why the mob turns to a dictator - to smash the machinery of the state that is no longer acting in their interest and resists all attempt at reform.
Congress has approval rates that are constantly in a toilet, and pretty much zero popular policies actually make their way into law. If they do, any popular implementation is stymied by an entrenched bureaucracy. Just look at the so-called infrastructure bill. Infrastructure spending is very popular, but instead of spending money to actually fix the shit that people use to run our society you saw Democrats musing about how 'trans rights
are infrastructure' in order to fund things that nobody wants instead.
The founders based a lot of the separation of powers on Machiavelli's
Discourses on Livy, and in that work Machiavelli's main thesis is that societies in the long term rotate between different forms of government which all become corrupt and are overthrown and replaced with another, so you should combine all three to ensure stability and therefore longevity (countries tend to lose ground to rival powers when weakened by the violent throes of transition). But no matter how well you combine them, there's no perfect government, and one arm of society will come to dominate. We're right now in the corrupted form of aristocracy (rule of the few), which is overthrown by the mob in order to institute democracy (rule of the many), which is incredibly unstable in its pure form, devolves into anarchy, and then you get monarchy (rule of the one). In Rome, you had a lot of populist, democratic movements which attempted to reform their system (the Gracchi being the most famous). These were all brutally repressed by TPTB, leading to increasing anarchy and eventually the rise of strongman figures like Marius, Sulla, Caesar, and Pompey.