Is the United States a stable government? Develop an argument using specific historical examples.

My answer to this question is, for the most part, yes—despite the imperfections the US political system has had and continues to have.
The current system under the Constitution has been in place since 1789, when Washington took office as the first president of the United States. During the 230 years since, there has been one attempt to break up the government, which was when the secession of Southern states occurred in 1860–61. In four years that attempt was defeated and the status quo ante was restored. Since then, as we know, the United States' system of government has remained stable with no further attempts to overturn it.
By contrast, during those same 230 years, many major countries in Europe and elsewhere in the world have gone through seismic changes. France's revolution occurred the same year, 1789, that the United States' constitutional system went into effect. Since then, France, despite its revolutionary ideals, became a dictatorship under the Directory and then under Napoleon, had a monarchical restoration of the Bourbons, and had a succession of upheavals and changes including Napoleon III's period and the temporary establishment of the Vichy regime in 1940–45, which was a puppet government of Hitler. Germany, which was not a unified country until 1870, went from a monarchy to the short-lived Weimar Republic to Hitler's Nazi regime to a divided state after World II, until finally, in 1990, it was reunified as a democracy (after the collapse of the Soviet Union). Most of the other large states in Europe have gone through similar upheavals. The United Kingdom has been stable since the eighteenth century, but its own constitutional system has evolved from one in which the monarchy still held a degree of genuine power, offset by Parliament, to one in which the monarch is a figurehead and the country is a genuine democracy.
All of these examples indicate the stability of the United States—again, despite the imperfections of its system—as compared to other countries during the same period. Though one could argue that the United States has been more stable because it is geographically relatively isolated and not nearly as susceptible to outside threats as European countries are, this doesn't alter the fact that its system of government has been stable under its constitutional system.