But I do think there is "An American Way" and that it reaches back to the very founding of this nation. The Revolution of 1776 was, we are told, based on freedom and the desire of the colonies to be free from a tyrannical government. But freedoms then, as now, are only realized in the physical world. Locke claimed that man had an inherent, or inalienable, right to "life, liberty, and the pursuit of property." Jefferson changed this to "...pursuit of happiness" and the change was a good one, but consider the connection. Happiness is closely tied to property. Locke's definition of the word included all those things which we lay claim to owning; body, ideas, foodstuffs, home & land, business, whatever we consider as an extension of ourselves. Without the ability to do with these things as we wish, in fact, without these things, liberty is only a phantasm and life is enemic. American liberty has, consequently, always been tied to materialism, for good or ill, so much so that the very revolution is actually a revolution of economics.
Materialism is mostly used pejoratively b/c, as the pope noted in Centesimus Annus, rampant consumerism dehumanizes people and causes a degeneration from democracy to tyranny of the rich over the poor. Thus Americans are frequently, and rightly, accused of lording their prosperity over poorer nations of the world and even over their own people. Nevertheless, to extricate freedom from property is an impossible operation. If one is free he must be free over some THING. Without property (goods, home, land, whatever) freedom is only a name. So I think first in the "American Way" thing is a sense that every man ought to have the ability to own property and exercise his liberty through such ownership.
Second, Locke claims, and Jefferson reiterates, that government exists for one reason only; namely, to secure inalienable rights. Rights to life, liberty and property exist b/c God made us so, not b/c some king or warlord allowed us such and such. Our government exists ONLY to make sure that these rights are honored by all, passing laws in order to perpetuate this security and levying taxes only to maintain its function. Government serves people, not people government. Thus, Americans ought to consider government intrusion a necessary evil which should only be invoked when other means have been exhausted. If the first element of "The American Way" is a right to certain inalienable rights, namely property, the second element is a vision of small government which ought not to interfere too much in the lives of its citizens.
Third, then, is the vision of self-reliance. B/c of our initial need to survive in a terrain which was challenging to say the least we have, as a nation, long held the opinion that a man must stand on his own two legs. We are not only able to make our own decisions, we are also held accountable for those decisions. No one ought to blame culture, race, handicap of any kind for the decisions they ultimately make and as Americans as much as we honor the decisions of others we also expect that they are going to take responsibility for those decisions. Included in this, I think, is an American respect for the opinions of other people and, thus, the ability to discourse rationally even with people holding opposing opinions.
Fourth seems to be an American talent for improvisation. We are always analyzing, reconstruction, tinkering and rebuilding everything; including ourselves. Part of our current fits of apoplexy are due to an intense need to refashion who we are following the trauma of 9/11. As much as I disagree with the naysayers of the war and with the conspiracy theorists, I know that what they are saying is part of the American thing. Americans are not "my country right or wrong"; that would be like a nation of automatons. Rather, we are "my country's successes, let me fix her wrongs." The inventions not just in technology but in cinema, foodstuffs, government & law, nutrition & science, production of goods, language, arts has been dominated by America for the last 200 years! Why? Coincidence? No, I'm in agreement with Victor Davis Hanson; the culture determines the culture. How we view ourselves determines what sort of culture we are, so that the dominance in invention is not circumstance by systemic in the culture.
Fifth, as we like to reinvent ourselves, we are also perhaps the one nation that has a sense of humor. Other nations certainly laugh, poke fun at things, enjoy life - I'm not saying they don't. But America has a remarkable ability, as a nation, for poking fun at herself and at others. We don't have the dementia of class-system or of race politics (for the most part) or of caste-system, we don't have open civil war in our streets (yet), we don't have grinding poverty or rampant disease (like Russia), we don't have forced abortions and a krypteia terrorizing our populace (as does China), we don't have the indolent wallowing in state-sponsored suicide as do most European nations. Consequently, we seem able, as a people, to laugh at ourselves; perhaps bitterly, perhaps jovially, but we laugh. Our entertainment industry, for all its faults, creates joyful works and works of great humor. We enjoy sporting events, gaming, leisure and group activities w/o fear that tanks are going to roll into the soccer stadium at any minute. Heck, we even find politics a sport and not something to riot over. Americans laugh. That's a good thing.
Now I know that these are generalizations; I know that the excesses of freedom allow for pornography, abortion, abuse, indulgence, addiction, corruption, and other really horrible things; I know that the government often oversteps its bounds and requires Dustin Hoffman and Robert Redford to correct it; I know that there are many people here in the States that are ignorant, arrogant, corrupt and brutal. All these things exist in any human culture. What I'm saying are generalizations, I know, but they are generalizations that work. If we are to look for the best things that make 21st America a better place to live than, say, Cuba, or Russia, or China, or ... France; if we are to look for the best things that make this country greater than Ancient Rome & Greece, or better than merry old England, or better than 19th century America, I think it would be these things; inalienable rights, view of government, sense of independence & responsibility, improvisation/improvement, and sense of humor.
Finally, with all the blemishes she has, I think the United States isn't just a fun place to live b/c we have lots of Burger Kings and Wal Marts. I really think that the United States, the philosophy that makes the nation more than a geographic location on Google maps, is invaluable and a treasure and ought to be exported to other nations willing to attempt the philosophy if not the excesses. Call me an imperialist slob if you will, but I really think, with Lincoln, that America is "the last, best hope of mankind."