The problem is not mountainous terrain, but rather that tracks usually proposed for Chicago-Florida service are either congested with freight traffic or have been significantly downgraded since passenger trains last operated over them. It's difficult if not impossible to cobble together a route that would not require major investment.
I have a hard time imagining that we'll see any sort of "direct" Chicago-Florida service (through some combination of cities like Atlanta, Birmingham, Evansville, Indianapolis, Louisville, or Nashville, as opposed to "indirect" service over existing Amtrak routes through New Orleans or Washington) until more of the states through which such a route would pass start operating corridor and/or commuter services. If we had some sort of Atlanta-based corridor system, with routes to Chattanooga and Jacksonville among others, and a Chicago-Indianapolis-Louisville corridor, then, at least in my opinion, it becomes much more plausible to get federal funding to reinstate a long distance train linking those corridors.
I have a hard time imagining that we'll see any sort of "direct" Chicago-Florida service (through some combination of cities like Atlanta, Birmingham, Evansville, Indianapolis, Louisville, or Nashville, as opposed to "indirect" service over existing Amtrak routes through New Orleans or Washington) until more of the states through which such a route would pass start operating corridor and/or commuter services. If we had some sort of Atlanta-based corridor system, with routes to Chattanooga and Jacksonville among others, and a Chicago-Indianapolis-Louisville corridor, then, at least in my opinion, it becomes much more plausible to get federal funding to reinstate a long distance train linking those corridors.