Jane Curtin and Al Franken are SNL alums: Curtin as a performer from 1975 - 1980, and Franken as a writer and occasional performer from 1975 - 2008.
Harry's hand gestures are imitative of U.S. Senator and 1996 presidential candidate Bob Dole, who would hold a pencil in his right hand while making a thumbs-up gesture with his left hand during speeches. Dole did this because he suffered severe injuries in World War II, including a debilitating one to his right hand, so holding a pencil kept people from trying to shake his painful hand.
Al Franken plays a shady politician. In reality, 12 years after this episode aired, he was elected to the U.S. Senate from Minnesota. It is implied that the character he plays is a Republican. Franken served in the Senate as a Democrat.
The episode title is a play on the name of the U.S. nonprofit, progressive-aligned organization Rock the Vote, established to encourage young voters to participate in elections. (Tjn - 10\10\2022)
Harry gets his first phone call in the show.