So I helped Garvey and then went out and cleaned up the Deathclaw and Raiders. When I returned I talked to him, said I didn't want to join and then, when crazy lady started blabbing, I moved away - ending the conversation.
After about 4 hours of play my character thought: well, maybe I will help them settle Sanctuary.....
I noticed they were still in Freedom Hall. So I travel there and no one will enter dialogue with me. I didn't get the Diamond City quest. So basically, if you interrupt crazy lady..... you're screwed out of at least the Minutemen quest line.
So, now I'm going to have to replay 4-5 hours of the game and make sure I listen to crazy lady.
Note to Bethesda: if you are going to "break off a conversation or even, shoot them in the face" then you might want to make sure it works and doesn't break the quest lines.