At first, you had me confused, since I think of Tommy as Governor Thompson, and you seemed to have been repeating yourself. Curiously, both Thompsons were the longest-serving governors of their respective states.
It sounds to me though that Big Jim was a little earlier than the other two. What if he gets elected as a dark horse in the early 90's (or late '80's after something unexpected happens to Reagan). Later, Fred Thompson gets elected in 2000, and chooses Tommy Thompson for a cabinet position (like Health and Human Services). Then, the unthinkable happens in 2001, and Fred, his VP, the Speaker, and a large portion of the cabinet are assassinated in simultaneous terrorist attacks. The first person in the line of succession to survive...Tommy.
Okay, it sounds kind of more like a satire than a realistic timeline. Although it kind of shows how really possible I think it is for Tommy to become president. Then, you've got to find a way to add in the other ten Thompson politicians I found on the Thompson surname wiki page... although probably not as president since some are from Canada and Australia.
Perhaps I should start a new thread to discuss rather than continuing to hijack this one? The gangster President here is interesting in its own right, and I'm sorry for polluting it with my misconceptions