There are three basic types of friction: kinetic static and rolling. When you slid the mass blocks around in physics, you were learning about kinetic and static friction, and all that F=µN stuff is true.
What rob is talking about is rolling friction. All forms of friction ARE dependent of surface area, but in kinetic and static, only very slightly. The force dependent on area is several orders of magnitude weaker than the µN force, so the formula is Ff = µN + really really small number. Rolling friction is almost entirely dependent on the weak forces. This is because the tire is technically not moving against the road. If it was, it would be skidding. Watch a wheel go for a bit -- the point in contact with the road stays on the same bit of road until it get lifted off of it. So when your tires start spinning, you lose the effect of having the extra area.
I will go look in my new physics C text tonight. Maybe i can clear it up. And if i am dead wrong, which i probably am, i apologize. But i do hold that you need to consider the difference between kinetic and rolling friction.
Take a look at these sites.
http://www.school-for-champions.com/...onrolling2.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html