"Great"? Well, that certainly opens a can of worms.
When people have called this country "great" in the more or less recent past (say, 50 years ago), I think they were expressing a number of things, including:
1) a feeling that things were going well for them, or would soon be,
2) combined with a pride in American accomplishments, such as landing men on the moon,
3) and perhaps a pride in American world leadership, along with
4) a sense that social, economic, and political progress was likely.
Most or all of those things don't seem to apply that much anymore. Things are not going well for most people. Lots of folks have lost hope they will ever be much better off than they are now. American accomplishments seem more on the order of smart bombs than breathtaking advances in other areas of the sciences and technologies. The country seems poised to lose it's position of world leader at some point perhaps not too far in the future to China. And we seem in many ways to be regressing socially, economically, and politically.
I believe the deterioration was primarily caused by poor leadership over the past 30 or 40 years. Notions like privatization, trickle down economics, radically free markets, and absolute free trade are recipes for eventual decline. Although such notions appeal to the child within all of us who wants a simple world that is easy to make sense of, it is lethal to apply them, as we have done over the past 30 to 40 years.
To me, greatness would be a society of genuine citizens, rather than mere consumers, active in their own governance, and creating a nation that was liberal in its rights, humane in its values, ecologically sustainable in its economy, and just and fair in its laws and their application. Those are my demands, and I consider them modest compared to my ideals.