I am looking at Nevada for example, I just find it very difficult to believe two counties decide for the whole state.
I'm not familiar with Nevada, but I instantly knew what one of those red areas was (Las Vegas), and looking on Google Maps, the other is Reno. Both of those are rather large cities in Nevada.
Let's look at some population numbers:
Nevada: 2,723,322 (
src)
Las Vegas: 583,756 city, 1,314,356 urban, 1,951,269 metro (
src)
Reno: 225,221 city, 694,960 metro (
src)
In other words, the area around and including those two cities accounts for about 97% of Nevada's population.
EDIT:
Zin, I don't really doubt the map; I just think he seriously misunderstands the population density in the areas that are marked as voting Democrat. As I mentioned, from what I can see, they're typically larger counties that include larger, or more prominent cities.