I think there are two things here, both particularly American in one degree or another.
First, American conservatism is very much drawn from American political traditions, history and mores, and yes, there is a great deal of American "exceptionalism" to it. That "exceptionalism, however, is rooted in the universal struggle of man, and oddly and ironically much more rooted in the major and profound historical, social, moral and intellectual thrusts of history - particularly European history - then the current order in Europe. It is the odd conundrum of America: Practical yet idealistic, visionary yet suspect of human nature, forward looking but in an intellectual and a moral sense more deeply rooted to Europe's past than the current European. It is difficult to explain this to Europeans (or even our version of them, the Democrat party.)
American conservatism harks back in the time of a basic philosophical divergence between Europe and the US in the late 18th century and the 19th Century: We came to understand the promise of the fall of the Ancient Regime - that the future was the common man, that man could rule himself. This is at once deeply visionary and deeply skeptical (almost bordering on cynical.) Europe,on the other hand, never really saw the way out. They merely sought to ape the old aristocratic order with a new one, replacing the old aristocracy with a new and "unnatural" one, and replaced the false gods of the failing old aristocracy with various new false gods. Fascism, Nazism, Socialism, "modernism," all failed in turn because they did not really face the crisis and the promise of the decline of the old European order.
This is what truly separates us from the European and it is even more pronounced because we have actually put our notion into practice and have gotten grand results. We are the Europe that might have been. In this sense we are more "European" then the Europeans are. When we say we "love Europe" and will defend "Europe" we refer to this grand, golden Europe that we sprang from, that we decocted and improved. The Europeans, of course, destroyed not only that Europe but that sort of European almost a century ago.
We are so close to this that we do not see how exceptional the American gamble is. The European is so close to the decline of his civilization that he cannot see the golden Europe which haunts him is gone never to return again.
The second point is that we actually believe in the nobility of man with all of his many sins, faults and limitations yet scarecly believe that he can be perfected. Improved here and there perhaps, changed to a degree over time, yet he is now and shall always be very much what God made him. And that is more than enough for us, given enough freedom and responsiblity everything will be fine and the best in man shall come forward. We feel this because our system has worked for a very long time - ironically enough longer than any other regime out there today. Our belief in mankind is not really idealistic but practical, yet it is still visionary. Mankind is not a project for us; no "new socialist man" in the making yonder. We take man as he is and understand that the liberties, talents, faults, wants and needs of the many, the few and the one must be balanced, and that the many, the few and the one all must have rights, duties and limits. There is nothing particularly mystical or even intellectual (in any systematic sense) about it. This is of course particularly irritating to intellectual and social elites in Europe for obvious reasons.
We are a common people doing uncommon things. This infuriates the European as much as it baffles him: He does not really believe it for he does not like man very much at all. There must be a catch - what is it?
Watching the EU evolve has given me much entertainment over the years as they get everything wrong, confuse effect with cause, symbol with substance and in general stand the reality of America on its head.
A single currency unites America and gives it power - let us create the Euro. No, It is a strong and united country that created the currency. They have big, expensive projects - let us get governments together and order built a bigger jet than theirs, a bigger rocket, a bigger atom smasher. No, it is the exuberance and the nature of the grand challenges that cause us to do these things, now we will move onto different grand challenges where size is not the issue but system integration and systems of systems is appropriate, just as size was appropriate. It is their dastardly control of the system, their constant gaming of it that makes them rich - let us build up a protected market in the EU and rule over it from Brussels. No, it is less government and less gaming of systems that makes us richer.
The EU is like a cargo cult, but the great white gods that so favored America are not coming, the bonfire are turning to embers.
The Europeans latest false God - "Europe" - is one of their more hilarious ones. Let us hope is is as harmless as it has been so far.
I must admit that I get some real amusement out of them. All the little snares, hierarchies and traps they lay for us yet once again we slip through the net and go on to yet another American future. It drives them mad.