They're not convinced because Clinton and Obama have sold them out time and time again. Affluent suburbia drags our party to the center because they care more about same-sex marriage than, say, the right to form a union or keeping manufacturing in the United States. They don't care about the worker.
You could say the same thing about many blue collar dems. They also care more about same sex marriage than union rights. Many let GOP cultural talking points cloud the economic issues that really matter. And between Obama and Romney, it's still clear that one man cares more about the average worker than the other one does.
Then we need to dig into the economic issues in the way we haven't. We've danced around the issue while supporting extended free trade agreements and allowed greater outsourcing. You win a voter group with a platform that appeals to them, and standing in favor of real reform and against the elites, the donors who control both parties, will give the Democrats a winning coalition of blacks, Hispanics, and blue-collar whites.
