"... we arrive at 496,804,500,000 square meters or 496,805 square kilometers (191,817 square miles) as the area required to power the world with solar panels. This is roughly equal to the area of Spain."

As was pointed out, that's the whole world, not the United States. And the Sahara Desert is 3.629 million square miles. Sounds like that would be a great place to site 200,000 square miles of solar panels. Of course, this would be infeasible for any number of reasons ranging from geopolitics to superconductors, which is why it's a thought experiment.

Someone's already on it:

http://en.wikipedia.org/wiki/Desertec

The most obvious problem being that transmitting the power from North Africa, to say Hawaii would pose a significant challenge.

Like I said, superconductors.

That figure is to power the whole world. The original questions was about the US, which requires a substantially smaller area.

My bad, that completely flew over my head. Thanks for pointing this out!