Define "greatest"...
Actually, most of the posters here have shown their awareness of how basic that is to the question. Certainly at the moment we are the single most powerful nation on earth. The richest man in the world, and a huge share of the other richest people, live here. We have the skyscrapers of Manhatten, the Grand Canyon and the canyonlands of Utah, some redwood forests we haven't cut down yet, and Preservation Hall is still intact in New Orleans.
And we have a proverty rate, down to the level of our infant mortality rate among the poor, that stands out among the "developed" nations: Largely because we have lost sight of major parts of the definition of greatness that we started out with.
The greater the degree to which we concern ourselves with who we are greater than, the greater the degree to which we have "blown it".