I'm not an engineer, but I'm sure something like this could be done and it would have mass appeal across the board.
As a country, we could use a way to get from point A to point B faster. HSR is a maturing field, so lets implement it, but at a more personal level. Basically, have stations where you could have your car attached to a HS rail car and you and your car are whisked away to your destination. You could travel from NYC to Chicago in a reasonable amount of time, be able to take your car and pack it, etc. Use RFID tags or something to designate origin and destination. Charge a toll for it, even a hefty one to justify the cost of building and maintaining it. In addition, design it for a mass transportation HSR use as well.
I don't like driving long distances, so if I could drive to Roanoke, put my car on a HSR system, and end up in Pittsburgh in 2 hours (I don't know how fast HSR is, so I made up a reasonable time for 160 mph), saving me 3 hours of driving and the stress of driving, I'd gladly pay good money for the service. Have stops outside of mid-sized cities and larger and run it nearly parallel to the current interstate system, which would still see heavy use.
I know its a pie-in-the-sky idea that would never see the light of day, but if we are going to upgrade infrastructure, might as well do it accomidating American's love affairs with their cars and giving them choices. I'm sure there are some issues with my idea, but I doubt it would be anything from an engineering stand point.