The government is supposed to be of the people, and for the people. The government should be subservient to the people, not the other way around (at one point in history, a novel concept).
The concept of the "American people" predates the current American government. It will survive the current American government (plenty of developed or developing countries have had multiple governments in the past century, without interrupting the notion of that country as a group of people. In the more distant past, consider France. France remained a country of the French, despite several dramatic changes in the nature of French government in the past 300 years). The people are the "fabric of America", not the government that the people have created. That government is just an imperfect tool used by the people.
The concept of the "American people" predates the current American government. It will survive the current American government (plenty of developed or developing countries have had multiple governments in the past century, without interrupting the notion of that country as a group of people. In the more distant past, consider France. France remained a country of the French, despite several dramatic changes in the nature of French government in the past 300 years). The people are the "fabric of America", not the government that the people have created. That government is just an imperfect tool used by the people.
That's the idea anyway.