What fun! This game reminds me of the game we played in the politicial science department, where you try to parse out the line of succession in the US government as, one by one, the successors get asassinated. I forget the number of successors, it's quite large, maybe Chris can remember.
In reality, when there is an address made by the US President to the Congress (such as a State of the Union address), it means that all of the successors are in one room at the same time. So, one person in the cabinet is designated to stay home that evening so as to avoid a situation where, say, the Architect of the Capitol has to assume any power.