The flat car has obviously taken it too far. It has very small tires, little to no suspension travel, and too little ground clearance.
But how low can you go? I say you're going to want about six inches of ground clearance to make it an all season car. You want the driver's pelvis about six inches higher still to allow a little bend in his knees while he sits on the floor. Beyond that, it's just a question of how far reclined you're willing to sit to reduce frontal area.
The Insight follows this formula pretty closely, and ends up 4.4 feet tall. Check out the seating posture:
I bet you could reduce height further with a prone recumbent seating position (lying down, face first). But you'd need a very low engine compartment in order to see over it, and you'd still need four feet of crumple zone in front of you.