The problem with train travel in the US is largely the rail network. I traveled from Central California to San Diego this week and the train had to stop and wait repeatedly. The trip took entirely too long. We had to wait for other Amtrak trains, MetroLink trains, and freight trains. We were stopped for up to 20-30 minutes at times, and were once stopped about 100 yards from a major station as we waited for a freight to pass.
If train travel is ever going to be competitive, efficient, or convenient the issue of track space and track right of way needs to be addressed. Imagine if while on a plane the captain said, "Ok folks, we've got to land at the next airport because the airway is being used by another plane. We'll be down and up off the ground as soon as we can." Amtrak has a disadvantage because it doesn't control its network, and its network is not prioritized like airspace or freeway networks by state and federal government.
Our rail network is not built or optimized for passenger rail, but rather for freight. Faster trains and cheaper fares won't make up for the notion and reality that you don't arrive on time and that it takes longer than it should to get from city 1 to city 2. Europe doesn't have this problem.
That said, there really are some nice benefits of train travel: little to no lines to wait in (show up minutes before departure), no security checks, more eco-friendly, can be cheaper, and I think it's more relaxing than flying.