I'd say the War of Independence is too early for that, at that point they still had the French, the Spanish, and quite a lot of the Native American tribes as relevant military opposition. Even the British were still on the continent as Canada didn't follow the 13 colonies, and war between the two did result in the White House getting burned down by British-Canadian forces prior to Canadian independence.

True, I am not that well versed in American history without reading it up. In a sense the US got lucky, that events elsewhere opened them the door to take over North America: the Napoleonic Wars and the sale of the French territories, the Spanish decline as a major power...