Been in this boat, got the life preserver.
Moral of the story is: be an educated and aware traveler. Pay close attention to your progress, and if it becomes clear you're going to miss-connect, don't wait for Amtrak to solve things. Get on the internet and check your options. Have those ready. Then call and get a reservation agent. Explain your problem and tell them the solution. Most times, they will need a supervisor to approve, but you get to have a say (and probably a bed). Did this and nabbed the very last bedroom between Chicago and New York for two days (on the Cardinal no less) for no additional charge from a roommate due to a blizzard shutting down the eastern seaboard while riding east on the CZ through Iowa. If I had waited, I would have spent the night in a Chicago hotel and ridden coach with a hundred others downgraded the next day.