This question really highlights Dogface’s point that the US had virtually no real foreign threat to expansion and the fact that balance of power politics dominated the era. We went to France to negotiate for the purchase of New Orleans, so we would have a port for the Mississippi shipping. France, instead, offered us the Louisiana Territory. Why? Well, because there were a considerable number of “westerners” in America that were quite ready to take it. The farmers in what was then the western fronteir of America needed the navigation of the Mississippi in order to survive.
France, almost undoubtedly, could have defeated an American incursion into Louisiana. Remember, at the time, France was a military power - quite unlike what they are thought of today. America had no real naval power at the time, and France could have landed troops in the territory, and based naval operations in the West Indies. However, the Louisiana Terrotiry really wasn’t of much importance to the French. The West Indies were a much more profitable area, and the attentions of the French nation were turning toward the creation of a European Empire (short, funny looking guy called Napoleon was involved in that one).
Here is where balance of power politics come into play. With both a Euorpean war raging and and an attempt to make a move in North America, Britain would probably have come down hard on the French. France and Britain were hardly on good terms at the time, and a large French army on the NA continent would certainly be seen as a threat to British Canada and the British West Indies. The British Navy would have descended quickly on French ships trying to move and support troops and would have made the defense of Louisiana very difficult.
Spanish power was rapidly declining and soon after this period they would be a non-factor (Mexican-American war 1840s, Sp-American war 1890s?) in detering American expansionism. British Canada was not really a threat at all. The war of 1812 showed that. The British push south from Canada was effectively checked, the southern push into New Orleans was thwarted and it was really only the front in the middle states that amounted to anything, as it was heavily supported by naval power (which Britain had in spades).
Not only was America largely free from the interference of European powers from the early nineteenth century on (unlike most other parts of the globe), the US was also able to maintain its own desired level of isolationism from the problems the European nations created for themselves. The US was free to develop on its own terms. Throw in a healthy supply (as already mentioned) of arable land, good climate, natural resources, and population and you get a ready recipe for success.
Then there is the American attitude of the period. To their minds, not only was greatness in reach, but it was the American destiny. Read what European observers (such as de Toqueville or Chevalier) said about the spirit of the American people; their drive, their enthusiasm, their undying belief in progress. I’m not saying that the drive for greatness is unique to America or to the time period, but it was a singular passion for the almost the entire population (or at least of the entire free population) and it really drove the American people. One example of this is the practice, during the industrial revolution, of the Americans to build their machines out of wood. They did this, knowing that the machines would soon wear out, becuase they believed that by that (admittedly short) time a better machine design would be available. They were always looking to a better future.
With this freedom from interference and the resources and attitude to make the best of the country, America could develop to the point that when, during WW I, it decided to enter forcefully into world politics, it had the power and ability to do so at the height of power. Again, when we entered WW II, we were able to do so on our own terms. At this point, the current (or recently past) situation developed. Europe had been through two devastating wars, on their own territory, in the past 30 or so years. Their populations, resources, economies, and infrastructures were destroyed. America’s, on the other hand, were largely untouched (perhaps made stronger). Asia and Africa were just beginning to see the end of the actual colonizations of their lands; the effects are still felt in most, if not all, of those areas.
Russia grew as a counter-point to America, but their country had been ravaged by the wars and by a series of revolutions the likes of which we haven’t had. The lingering effects of the czars and the feudal-like state were still being felt. They had never fully industrialized, and skipped past capitalism direct to socialism/communism. This was not an economically good move. The driving force behind their actions was ideology, and one that most in the country probably did not believe (as the corrupt nature of most people kept it from being fully implemented). It was a hollow(with the very large exception of the development of nukes) threat to American supremacy, and rather than cehcking the growth of America, Russia fueled our rise.
With the collapse of the USSR, there was a power-vacuum as a nemesis to the US. It won’t be filled for a very long time, if at all. Asymetric battles will now be the rule whenever the US is involved. I see a parallel between our position and that of Rome at its height. Their will be skirmishes and threats in hot-spots across the world, but no real enemy we can march against (or who can march against us). The major difference being that the American Empire is not one of lands, but cultural and economic. Like Rome, we will fall - not at the hands of an equal rival, but by overextending our reach, schisms at home, and opportunistic thrusts by less powerful enemies. Only then will American power be within striking distance of another nation or confederacy.