Functionally, while the President appears to be the great decider, the mob is far more powerful -- they can block the President from firing someone or fire the President with a with a simple majority.

So the week part of the game is a social deduction game; non-traitors try to figure out who the traitors are and advise the President (or consent/refuse to consent to firings); traitors do the same except that they're trying to look like non-traitors.

During the weekend, everyone closes their eyes -- except the traitors, who designate their target for the weekend.

And yeah, the Spades=Trump thing is the opposite of accidental.