Coss,
Eighteen hours and about $280 for a roomette, from Chicago to Longview, Texas. If you want to do a coach seat, it can be done for about $100 one way. From Longview, you can take an Amtrak bus to either the airport or the bus station in Shreveport. I did a round trip on the Eagle last November to visit friends in Texas. Weather and track work in Illinois played hob with the schedule, but I still enjoyed the trip. I tucked into the roomette with a good book, a small bottle of Makers Mark and a thermos of ice.
Another nice thing about the roomette is your meals in the diner are included. My wife and I have seriously discussed the Empire Builder from Chicago going west, with a stay at Glacier National Park, and maybe then the Coast Starlight to LA and then fly home from there. My friend in Texas and his wife have done the Coast Starlight, and loved it. There's a lounge on there for the sleeper passengers that shows movies in the evening.
(There's a 10% discount for over 62 as well.)