The pressure the car applies to the floor is a function of the weight of the car and area of the car's tires. This pressure cannot change unless either the weight or the area of the tires changes. Under normal conditions, the answer is 'no'. Whatever the area of the tires that are on the ground will also stay the same no matter how fast the car goes. But, all of this is only under normal conditions.
Some cars have spoilers on the back end.
Well, if a car goes fast enough and if the spoiler is designed correctly the car will have the opposite of what an airplane has to make it fly. Call it anti-lift. The shape of the spoiler causes the car to have more weight sue to the flow of air over the spoiler. So, the faster the car goes the less chance it has of flying. You could do this but the lift would not be nearly enough to raise the car off the ground.