Once upon a time there was, in fact there were weveral. At this point, there is unlikely to be one again anytime soon because the railroad routes between the midwest and Florida have veavy freight traffic, and are relatively slow due to the curves in the Appalacians.
When Amtrak came into being there was a pair of every other day Chicago to Florida trains. Amtrak took the South Wind route, Chicago, Indinapolis, Louisville, Nashville, Birmingham, Montgomery, Dothan, Waycross, Jacksonville, and on to Miami and St. Petersburg because of the larger on-line population, made it daily and renamed it the Floridian. It's existance was somewhat of a soap opera that ended with the Carter cuts. After its demise, there was from time to time a through coach between the Capital Limited and one of the Florida trains. Capital going Superliner makes that no longer possible.
The Floridian's route across Indiana is partly abandoned, but a Chicago Indianapolis to Louisville train is still practical IF the rail between Indianapolis and Louisville is replaced. The rest of the route is still in place, but Montgomery to Waycross may require considerable work before the former 59 mph passenger speed can be reestablished.
The former heaviest used train, the City of Miami, Chicago, Carbondale, Jackson, Tennessee, Birmingham, Columbus, Georgia, Albany Waycross, Jacksonville and on to Tampa, St. Petersburg and Miami is no longer possible as segments between Jackson and Birmingham and Albany and Waycross have been abandoned.
Up until the 50's and early to mid 60's for some, there were several basic businessmen's overnight trains from Chicago, Cleveland, Detroit, Pittsburg, etc. that converged on Cincinatti. These contributed sleepers, and from a few origins, through coaches, to form two Cincinatti to Florida through trains, The Royal Palm via Southern and the Southland via L&N. Both these trains were daytime trains to Atlanta, with the Palm arriving Jacsonville early the next morning, with mid afternoon arrival in Miami. The Southland was a West Florida train, with Jacksonville and Miami passengers having to change to the Dixie Flyer at Atlanta. In their later years, a change of trains at Jacksonville was required.
It will take a level of investment in track that seems unlikely to occur under present circumstances to increase capacity and speeds to the point that any of these midwest to Florida services would again become practical.
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