The American order is complex -- it is much more sophisticated than "democracy," which assumes that nothing stands between the individual and the national state except aggregation, that might (defined as 50 percent + 1) makes right. The American order is based on the idea that the United States consists of many different kinds of people in many different kinds of communities, and that each of these has interests that are legitimate even when they conflict with the equally legitimate interests of other communities. The densely populous urban mode of life is not the only mode of life, and the people of the urban areas are not entitled by their greater numbers to dominate their fellow citizens in the less populous rural areas.
The basic units of the United States are, as the name suggests, the several states. The states created the federal government, not the other way around. The states are not administrative subdivisions of the federal government, which is their instrument, not their master. In this, the United States is fundamentally different from countries such as the United Kingdom and Japan, which have unitary national governments under which provincial distinctions are largely irrelevant.
In our system, the states matter. Under the Democrats' vision, some states matter: California, Texas, Florida, New York, Pennsylvania, Illinois, and Ohio, which, without the institutions of federalism, have among them the numbers and the power to effectively dominate the rest of the country.
At the time of the Founding, the people of the smaller states did not desire to enter into a union in which they and their interests would be dominated by the larger ones. The people of the smaller states still do not wish to be politically dominated by the larger one. For that reason, the interests of the states as such -- not mere aggregates of voters -- are taken into consideration. The Senate, as originally organized, existed to preserve the interests of the states as such against the opportunism and predation of the more populous House of Representatives -- and against the ambitions of the executive, too. Turning the Senate into an inflated version of the House was one of the progressives' first great victories against the Constitution of the United States and an important step toward the sort of mass democracy that our constitutional order is explicitly designed to prevent.
But the states have other protections as well, one of which is the Electoral College, which helps to ensure that the president -- the Founders were right to fear presidential ambition -- is not a mere tribune of the plebs, a rider upon "the beast with many heads" empowered by the mob at his back to abuse and dominate members of minority groups -- smaller states, religious minorities, political minorities, etc.
The rights of minorities are further protected -- from democracy -- by the Constitution's limitations on the power of the federal government and specifically by the Bill of Rights, which places some considerations above democracy: freedom of speech, freedom of religion, freedom of the press, the right to keep and bear arms, the right to security in one's home and papers, etc...