Believe it or not we already have this. It's an Amtrak train between DC and central Florida. You are a passenger aboard the train but your car comes with you! http://www.amtrak.com/auto-train
This is not a cheap stab at US rail, I looked into this on the similar service that the German railways offer - and it did not make financial sense over flight+rental.
Think 100% electric high speed trains that let cars 'board' at highway speeds. Evacuated underground tunnels for low drag long distance high speed trips. Hybrid Maglev cars that rocket down the highway on a cushion of air while being inductively charged. Even things as simple as highways without road signs of any kind.
That's interesting because while I've heard of and thought about the concept of a vacuum tube train that could go ridiculously fast, I didn't think of a merely low-pressure tunnel that ordinary cars (with pressurized compartments, anyway) could use in flexible manner. You wouldn't go 15,000 mph, but you could do several hundred pretty easily.
Alternatively, in say 20 years or so, going to Miami which would take 21 hours (at 65-70 mph), could probably be done on an overnight sleeper-car (at probably something more like 120-130mph).
Even a cross country trip would only take a day or so at such a rate, and with a few strategically placed stops, you could have a nice week long cross country trip at a fraction of the normal cost.
Here's a few negative thoughts though:
These driverless cars might significantly increase road usage and wear since driving becomes less of a burden.
Suburban sprawl could grow out of control since it's no longer necessary to either have public transit options or be attentive to have a long commute.
Some people might even choose to buy automated RVs instead of homes, decreasing a sense of community and investment in place.