I know very little about the constitution of other countries. In America we are taught or led to believe that ours is unique. I knew one person, a religious man, who argued the American constitution was divinely inspired. As you know I am an atheist, so I would not go that far, but we are convinced that because of our constitution we are assured representation in our government and established a system of checks and balances. Freedom from the King and dictatorships. Not only our constitution, but other documents like the Declaration of Independence, even the poem on the Statue of Liberty, are seen as very important, and those who wrote them as inspired.
America is a country of immigrants for the most part, and so most of us take very seriously the idea of being created equal, religious freedom, separation of church and state, and we are led to believe that we were one of the first countries to come up with such a notion. Many of use knew personally our relatives who left desperate situations in their previous countries, who are grateful for the opportunity America provided, or are immigrants ourselves.
Moreover, I would say we are constantly told there is no better country, and no similar country through media, teachers, and others (I would say that this was more true years ago). Also, we frequently refer to the constitution to evaluate whether a law should be law. So, I guess since we tend to feel grateful for the country we live in, we also treasure the documents and rules of law that provide us with the life we have in America, and therefore also revere the people who wrote the intitial documents establishing our country.
As a disclaimer I would like to say that my worst subject in school was history, not far behind was government, although I have become much more interested in these topics as I got older. But, I was raised that America is a paradise. I am 2nd generation American on one side and 3rd on the other, and married to someone who is an immigrant himself. Being Jewish definitely had a big influence on this. Feeling safe in a country, having equal rights, knowing people who had come from all over the world, many different races, religions, ethnic backgrounds all living together, all citizens. America has not always lived up to its ideals of the constitution and other intentions of our founders, but we strive for it.