I'm envisioning the United States as a rectangle 1000 miles high and 3000 miles long. I'm not including Alaska, because, although it's large, it doesn't have many roads. Much of the U.S. is rural, so roads are fairly sparse. In the semi-rural area of New York State where I grew up, it was common to go a mile or so without hitting a road. So it's reasonable to imagine the U.S. as a grid of roads, each one mile from the other.
That means that if all roads were evenly distributed, the U.S. would be covered with a grid of 1000 roads of 3000 miles each, and 3000 roads of 1000 miles each, for a total of 6,000,000 miles of roads.
Editor's Note: Not bad, according to National Atlas there are about 4,000,000 miles of roads in the U.S.