So you are referring to the political theory version, where the US was founded on free enterprise, and republican rule?
From wikipedia
American exceptionalism is the theory that the United States is qualitatively different from other nations.[2] In this view, U.S. exceptionalism stems from its emergence from the American Revolution, thereby becoming what political scientist Seymour Martin Lipset called "the first new nation"[3] and developing a uniquely American ideology, "Americanism", based on liberty, egalitarianism, individualism, republicanism, democracy and laissez-faire. This ideology itself is often referred to as "American exceptionalism."[4]
This is just nationalistic sensationalism, on par with the British notion of Empire from the day. While it's true that the British version had more of a feudal flavor involved, and the US version has a more Fascist overtone, the basic notion at work is the same. "My nationality is the bestest ever, and deserving exceptional treatment because [convenient reason]." You'll find it everywhere that there is a strong government trying to justify its political actions against political rivals. I prefer the more generic moniker of "Nationalism," personally.
In the scope of it describing some uniqueness to the "american way of doing things" (culture, art, philosophy, whatever), it still is just puffery. Yes, the US way is unique. Just like all the others. The US is NOT the first country to try rule by plutocracy (originally through republicanism)-- Rome did it first. It lasted a while, but didnt end well. Same issues with nationalism.