Bill,
As I promised in chat, here you go.
Your sleeper tickets qualify you as a First Class passenger on Amtrak. As a first class passenger you are entitled to utilize Amtrak's first class lounges in DC and Chicago. These lounges are a nice quiet refuge in the often-bustling train station. They have nice plush chairs, conference rooms, computer terminals (DC only), newspapers, TV's, free soft drinks, juices, coffee, tea and clean safe bathrooms. They also allow you to board your train before the rest of the masses.
In DC the Club Acela Lounge is located behind the information kiosk, which is in the center of the waiting areas between gates D & E. There are two large wooden doors there, ring the bell to the right of the door and the attendant will let you in. Show your tickets and you’re in. They will escort you to your train when it’s time.
There is a place that you can leave your luggage in the lounge, right behind the checkin counter. Note that this area isn't really guarded, like Chicago's, but I've never heard of any problems with missing luggage
In Chicago the lounge is called the "Metropolitan Lounge". It is located on the lower level of Union Station, which is also the track level. If you are standing in front of and facing the Amtrak ticket windows, then the Amtrak waiting area is to your left. When you enter the main Amtrak waiting area through a sliding glass door, just walk forward and slightly to the left. There should be another sliding glass door along with a sign. Again, just show your tickets and relax.
In Chicago they'll give you a pass that you can use to come and go as you please, without the need to check in again. This will allow you, assuming an on-time arrival, time to wander around the station and perhaps the city, if time permits. Just make sure that you're back in the lounge by the time written on the card.
As I mentioned, you can also leave your luggage there too. There is a room within the lounge, staffed by a redcap, where you can check your bags before wandering around the city.