I did <any research at all> and found the following in case anyone is interested:

   1. It appears Amtrak sleeper cars accommodate between 30 and 50 people.
   2. An Amtrak coach car seats up to 80 people (fewer than I expected).
   3. So to switch everything to sleeper cars would require trains to be 2-3 times as long.
   4. A typical Amtrak train is 11-12 cars long, and each car is about 85 feet long. 
   5. So Amtrak trains are currently about 1,000 feet long, which means they could be 2-3x as long and still be *well* under a mile long.

This seems easily doable. As others have pointed out, super-long trains have a number of issues, but trains could accommodate almost 2x the passengers, and be all-sleeper, and still be only a mile long. Then you run multiple trains to handle the larger demand!