Good question. When Mr. Obama was speaking about Milk, that man was already dead. And Obama was talking about something (Milk's election) that happened to Milk while he was still alive and that was later in his life than that time when he (Milk) was first trying to get elected. This use of "would" is caled "future in the past."
("Had" describes something that happened or began in the past . But Obama was talking about an event in Milk's future.)