The City of New Orleans is a train
operated by Amtrak
; as the song suggests, it serves the route between Chicago
and New Orleans
It no longer leaves southbound on the "Monday morning rail"; you'll have to catch the 8PM departure from Chicago, because by the morning (6:30AM) you'd have to be Walking In Memphis to catch this train.
The good news is that you'll arrive in New Orleans in the mid-afternoon (3:40PM), with time enough to beat rush hour and head down to your favorite places.