The solution as I see it for Democrats is relatively simple (though the execution, as is so often the case, will be very difficult).
Number one, they must look inward and refine the principles and values at the core of the Democratic Party.
And number two, they must learn again how to draw a line between the those principles and values and the daily lives of average Americans.
1. Refining values
The Democratic Party has lost its way in trying to be all things to all people; even if you wanted to argue the point, it is the perception for a large swath of the voting public and perception in politics is, for all intents and purposes, reality. Environmentalists, pro-choicers, civil libertarians, trial lawyers, labor unions, teachers, all have a home in the party. It is its strength, to be sure, but also its weakness.
What is the Democratic Party? Too often these days, the closest definition is "We're whatever the Republicans aren't." All that does is allow others to define yourselves. If they hold position A, the Democrats appear to reflexively hold position (not A). Where does that put us if the Republicans happen to be right? (Centrists suffer from the same problem, at least as strictly defined--if they position themselves as a matter of principle squarely between Republicans and Democrats, then their stances will change as Democrats' and Republicans' stances change.)
The solution to that is to nail down the values and principles that make up the core of the Democratic philosophy. Where those should intersect with Republican values, that's great--action will take place, because they'll all be in agreement. Where the Republicans should disagree, then we get the benefit of honest political debate.
From time to time and issue to issue, various groups will pull in the same direction as Democrats and sometimes against, but by always keeping an eye on the philosophical North Star, the Democrats at least will be secure in knowing the direction they should be moving in.
The process of cementing those values and principles will mean losing some people from the Party--which, honestly, is as it should be. Definition is (by definition) about describing the nature of some thing--what it is, and therefore what it is not. For a political philosophy that means that some perspectives won't be retained.
(One of the great strengths of this country, too, is that the people thusly excluded will be able to form their own voice and compete in an open marketplace of ideas, and they may become a group that works with the Democrats on issues of common concern.)
When was the last time a Democratic candidate said "If you disagree, you shouldn't vote for me"? If the Democratic values and principles are clear, this will happen and they should be proud of it.
What are those values and principles? This is the conversation that now must be had.
My personal opinion is that the best values and principles are the following:
1.) A strict adherence to civil liberties--freedom of speech, freedom of assembly, freedom of the press, freedom of worship, etc.--and then of the well-informed democracy that is ultimately the best guarantor thereof.
2.) A fundamental support of the notion that "all are created equal."
3.) A belief that education is the best means to preserve and extend our liberty.
4.) A belief in the ongoing progress of humanity, that tomorrow can always be better than today.
5.) Building off of #1, the notion that many ideas are better than one, and only through open debate in the marketplace of ideas will the best solutions emerge. Thus a stance in favor of multiculturalism, engagement abroad, any open exchange of ideas (which is why freedom of speech, of assembly, and so on are so critical).
The values and principles to which members of the Democratic Party adhere may or may not be grounded in the individuals' faith traditions. I suspect a many people of faith are driven to the Democrats because of and not despite their faiths. Concern for the poor has a prominent place in Christian scripture, for instance. Whether a Democrat argues from scripture, from Natural Law, or from a strict sense of utilitarianism, Democratic values have to resonate with people's core values.
And they must represent to the world the moral conviction upon which they are based. Robert Reich had an NPR commentary on just this subject the day after the election (transcript and audio).
As a part of the Democratic Party's redefinition, they will (and must) stop being "the party of special interests." Again, even if it's not strictly true, it is the public perception. The public sees the list I mentioned earlier (trial lawyers, unions, etc.) as driving the party, rather than occasionally working side-by-side with it. There may be philosophical agreement between group and party, but the party ought to be separate. And as the core philosophy is defined, some of those groups will naturally be sloughed off.
2. Drawing the line
In reading the passionate commentary after the election, it is clear that the thought among many Democrats was that the public would see the economic self-interest they have in the Democrats' position, and vote accordingly (that is, for the Democrats). What they failed on is that economic self-interest isn't the only thing that drives people into the voting booth or directs their hands once they're there.
Moral self-interest, if you will, was a large motivator in this election, as countless post-election articles have already told us. But in some ways, the question is even less complex than that. It is a question of resonance--whether the values being espoused by a party or candidate resonate with the values the voter holds.
This is why it is imperative that the Democrats learn to show how the Democratic values--civil liberties, education, care for the poor--are already in harmony with values the voter feels every day. Democrats need to learn to draw a line connecting their stances on issues with the voters' own lives. It is not enough to simply show them the Democratic values and assume they'll make the connection; the connection must be made for them. The horse can't simply be shown there is water--it must be led to it--and hopefully, then, it will drink.