Originally Posted by Ispolkom

Amtrak doesn't care, and there isn't TSA-like security to worry about. I think the rule is that you should be there at least half an hour before your departure, but I've caught the 4:05 p.m. Capitol Limited after arriving at Union Station at 3:57. I don't recommend cutting it that tight, but it can be done.

Remember that if you do have time to kill in either DC Union Station or Chicago Union Station, as a sleeper passenger you can use the Club Acela (in DC) and the Metropolitan Lounge (in Chicago). Heck, if you're coming from New York or Philadelphia on a regional, you can use the Club Acela there by showing your same-day sleeper ticket, even though you're leaving that station on a regional train.