The main problem with rail is not necessarily speed. Current Amtrak trains are slow and painful because:
- They stop everywhere. There are hardly any express trains that run between major cities. This punishes the majority of inter-city travelers by forcing them to stop at every little village along the way, making the whole trip unbearably long compared to air, or even car.
- They share track with freight. I cannot count the number of times the train would stop just to wait for some 100-car freight train to pass. Passenger rail needs its own capacity, not piggy-backing on top of industrial rail.
You fix these two problems and instantly the majority of inter-city rail travel will suddenly already be competitive with air travel - and completely destroy car travel in terms of convenience and cost, for short to mid haul routes anyway. All of this without laying a single mile of special-gauge track, ludicrously expensive trains, and all using off-the-shelf, mature technologies that don't cost a quarter as much.
The solution to America's transportation woes IMHO is not sci-fi level technology. Yes, HSR may be justified in a few places, but for everywhere else, I think good old fashioned overhauling the existing rail system would do wonders.