No.

The total amount of solar radiation striking the earth's atmosphere, in full sunlight and at the point nearest the sun, is around 1,368 watts per square meter. Averaging this out for both the rotation of the earth in the day / night cycle as well as the tilt and eccentricity of orbit during a full year, the average incidence over time is about 342 watts / m2. Some of this is reflected by the atmosphere, so by the time we get down to ground level, we can count on about 240 watts / m2. That's total energy, ignoring conversion efficiency.

Now, in 2008, the US consumed 4.369 petawatt-hours of electricity. That's 4,369,000,000,000,000 watt-hours per year. (We're #1!)

At a theoretical 100% conversion efficiency, an "average" solar collector would have to have an area of 18,204,166,666,666.7 square meters to capture that much energy. That's 7,028,668 square miles.

For reference, the entire continental US is only 2,959,064 square miles.

The most efficient EXPERIMENTAL solar collector presently in operation is the Tessera Solar SunCatcher array in Maricopa, AZ. This system, which reflects solar energy onto a Stirling engine, holds the world's record for solar conversion at 31.25%. It sits on 1,525 acres and generates a paltry 1.5 MW AT ITS PEAK. (By comparison, the San Onofre Nuclear Generating Station occupies 84 acres of land and generates 2,340 MW all day, every day, rain or shine.)

So, assuming we used this same 31.25% efficient technology, and assuming we figure out a way to make the dishes square so that not a single bit of area is wasted between them, we'd need to construct an array which occupies 22,491,737 square miles to satisfy the US's electrical needs. That's 40% of the entire dry-land area of the earth.

Obviously we can decrease this if we bunch all the dishes together in a band around the equator rather than distributing them equally, but you're not going to get an increase of SIX ORDERS OF MAGNITUDE out of that. If the amount of solar energy striking Phoenix were one million times greater than the amount of energy striking an "average" city such as Toronto, the entire state of Arizona would have long since sublimated into its constituent subatomic elements. And, of course, we'r only talking about the US here. Other countries need electricity, too. China, for example, is only about 2-3% behind us right now, and will overtake within a couple of years.

So I'm afraid I'm going to need to see a citation quoted to support the 32 square mile claim.