What were the key social, economic, and political changes over time from the 1770s to the 1860s? In my paper, I want to take into account the idea of who is an American and arguments over America's destiny, the changes wrought by the market revolution, and the arguments over the role of the federal government.

There were many social, political, and economic changes in the period from the American Revolution to the Civil War (1770s to 1860s). You might want to focus your thesis on the argument over the size of the federal government as the country's economy was undergoing the market revolution and the first wave of the Industrial Revolution and the country was becoming an economic and military power.
The argument over the power of the federal government went back to the period of ratifying the Constitution and the debate between Federalists and anti-Federalists (the Anti-Federalists later became the Democratic-Republicans and then the Democrats, while the Federalists later became the Whigs and then the Republicans).
If you divide your paper into three body paragraphs--economic, social, and political divisions and developments--you can speak about the political debates between the Federalists, who wanted a strong federal government (as did their successors), and the Anti-federalists, who were proponents of states' rights. Economically, the Federalists embraced the market revolution and the first wave of the Industrial Revolution, while the Anti-federalists, such as Jefferson, wanted a return to agrarianism. Socially, the Federalists were composed of industrialists in the Northeast and along the coast, while the Anti-federalists and their later political incarnations (that is, the political parties that grew from them in time) were largely composed of farmers, small artisans, and working people. The parties were divided over many issues, including whether the U.S. should expand (an idea generally supported by the Democratic-Republicans and their later incarnations and opposed by the Federalists and their later incarnations). In each paragraph, you can incorporate documents such as the Federalist Papers (if you have read that) and other sources from your coursework.