Uh...you better put that car on a treadmill

In theory, a car moving at 60mph in a straight line with a tailwind of 60 mph would see no signifigant wind resistance except for the part like the wheels, driveshaft, etc. The forces cancel each other out.
Think of the air mass like a block of jello moving at 60mph. If you are moving forward at 60mph and the block of jello is also moving at 60mph, then there is no relative motion except for the wheels and other rotating parts.
Here is another way to think about it - if you open the window on the highway and stick you hand out, you would feel relative wind. If there was a perfect tailwind of 60mph, then your hand would feel no wind. There is also no relative wind acting on the car.
Of course in reality, I think that a perfect tailwind of 60mph would still have a very very small effect, the wind flowing under the car, the wind flowing around the wheels, it would all mess up the air moving around the car and it wouldn't act like a block of jello, it would act like a block of jello with little disturbances all around it. BUT the overall effect would be so small that it would be insignifigant compared to the effect that different car shapes would have, etc.