AUGUSTA, Me. — Three years after voters in Maine rejected same-sex marriage, they will consider the matter again in November. This time, advocates say they have reason for optimism. “It’s about love and family,” says Ms. Nugent, seen with Sam Lundquist, a Falmouth resident. Carroll Conley Jr., at his office in Augusta, is executive director of the Christian Civic League of Maine and a leader of the opposition campaign. They point to a shift in public opinion, the personal support for same-sex marriage voiced last month by President Obama and what they believe is an effective door-to-door “persuasion” campaign throughout...