Picture a 1-foot by 1.5-foot rectangle on the ground, and picture someone standing on it. Now picture a lot of these rectangles blocked together on a flat surface, each with one person standing on it. Nobody would be touching anyone else-- the larger people might take up a bit more space, but the smaller people would take up a bit less, and the given space would be more than enough, on average.
If you drew a square mile on the ground and filled it with these rectangles, and put a person on each, you could fit over 18 million people in one square mile, with no one touching anyone else.
There are about 280,000,000 people in America, so you'd need about 15 square miles, or a 4-mile by 4-mile square, to accommodate the whole nation.
And of course, I'm not going to stop there.
There are about 7 billion people in the world. Since each square mile can fit about 18 million people, you'd need about 375 square miles to fit everyone. A 20-mile by 20-mile square would easily suffice. Let's be efficient, though. What if you took each of these 375 square miles and stacked them on top of one another. On average, you'd need a bit under 6 feet per stack (again, taller people would be in higher stacks, shorter people would be in shorter ones, and it would average out), so all the stacks together would be about 2,300 feet high. Stacking these square miles would form a building with a square mile base, about 2,300 feet high. The world's tallest skyscraper, in Taipei, is just under 1,700 feet. So our building would be just a bit taller than the biggest skyscrapers.
You could fit the whole world in that building, without anyone touching anyone else.
I'm not sure what point I'm making here-- that people are little, or that it's a small world, or that 7 billion is a relatively small number of people, or that 7 billion is a huge amount of people but people are damn little, or that "overpopulation" is funny, or that a square mile by 2,300 feet is a shitload of space to work with, or that the building would smell horrific.
Either way, chew on that for awhile.