Americans were born arguing. The big challenge 200 years ago was to make a fractious people into a united nation. That's a challenge that will never go away. Most of us no longer believe America would be better off as a number of regional confederations - as many did back then - but we disagree about today's issues with the same passionate intensity.
In Federalist No. 1, Hamilton complained that both sides of the ratification debate seemed to think they could convince voters of the "justness of their opinions ... by the loudness of their declamations and the bitterness of their invectives" - a characterization that could apply to almost any modern cable pundit and many of today's politicians.
Government is obligated to harmonize our clashing interests. According to Madison, that's what we elect Congress to do. In Federalist No. 10, he noted perceptively that economic inequality is a "durable source" of social conflict. "Those who hold and those who are without property have ever formed distinct interests in society," he wrote. "The regulation of these various and interfering interests forms the principal task of modern legislation."
The framers' goal was to design a system of government that moderated "the spirit of party and faction" flowing from that clash of interests. They knew that disagreement was a necessary and ordinary part of the political process, but they sought to create a government capable of bridging divides to advance the common good.
The Constitution invites us to elect officials who can do that. One of the benefits of living in a big country is that it teems with talent. The electoral framework the framers devised would (they hoped) elevate the most talented politicians to national office.
What, in their view, separated the best politicians from the rest? First, an ability to identify the common good. And second, a willingness to set aside narrow interests in favor of what's right for the nation as a whole. As Madison imagined it, we would elect congressional representatives "whose wisdom may best discern the true interest of their country, and whose patriotism and love of justice will be least likely to sacrifice it to temporary or partial considerations."