Just an idea...Turn the 3 Senate cards face-up at the beginning of the round, and explain what they mean to everyone. It shouldn't mess up the game too much, and it will save that awkward pause as players stare at those cards and try to decide which ones to take. It might even add a cool strategy because you could see what the cards are worth to others and play to block them from getting one.

Ok I get the senate cards now, they are hard to understand at first, the the occupied or unoccupied bit got me but I was also trying to figure out the rules and teach my girlfriend while learning at the same time, so its to be expected I think.

I now feel its better to just flub your way through a game right or wrong and count the score also right or wrong then go back over the rules and figure out what you did wrong, in the end you will learn faster.
I tried to learn the game by just reading the book and it did not make sense to me but after the first game it was good.