|The Empire Builder near Glacier National Park, Montana|
Judging from the number of freight trains that were constantly being passed on some lines, it seems the capacity problem wasn't confined to that, and the freight railroads confirm that their premier lines are now operated at or near full capacity.
The issue becomes one of who pays for the extra track capacity; the freight railroads naturally want to increase capacity for their own needs but expect Amtrak to pay for that needed for their passenger trains. Federal law allows Amtrak to run passenger trains where and when it likes, providing it does not unduly delay the host railroads' freight trains, however, that is becoming more and more an issue.
The other situation where capacity becomes a problem is at stations: longer trains need longer platforms, and that applies everywhere. At the big city stations passengers need to walk to their car from a central boarding gate; except on the Northeast Corridor you don't just show up at a platform and get on a car of your choice as you do in Europe. That can mean long walks, but at the least the platforms (at this stage) are long enough to accommodate long trains. That isn't the case at many intermediate stations and sometimes the train has to stop at a specific point where there is a car with spare seats where people can get on and off.
President Obama wants to spend more on the passenger train infrastructure to deal with these issues, but, of course, is up against the inevitable Congressional Republican opposition.