What is the name of the group of individuals that have the responsibility of electing the president of the US?

I believe the answer to what you are asking is called the Electoral College. It is other wise known as Winner-Take-All. It means you, as the president get so many votes per state. In that one (1) state, say Obama got 25/40, he would win that state over because he got more of the 40 than McCain.: )