The Democratic Party has a love hate relationship with Christianty. On one hand, it hates the Pat Robertsons of the world (the feeling is mutual). On the other hand, it would like to love liberal and mainline Protestants, Catholics, black Christians, and even those evangelical white Christians who can see beyond the twisted ideas of their most prominent leaders. In many of these cases, however, the feeling is not fully reciprocated.
The Republican Party is pretty much the white straight Christian party. They make some token concessions to the contrary, but tokenism is about as far as it goes. Republicans open their events with Christian prayers, and adopt policies that drive out any sane gay man or lesbian woman (who isn't so filthy rich that tax cuts don't override everything else), as well as most people who aren't white. Even the Joe Lieberman's of the world (he is an Orthodox Jew from Connecticut with strong bipartisan inclinations on high profile issues), who sympathize with Republicans on many moral and religious issues, ultimately, as non-Chrisians, feel more comfortable as part of the Democratic party. The Democratic Party is far more pluralistic. It is ethnically diverse, embraces gays and lesbians as well as straight people and is not a Christian party. It isn't anti-Christian, but as the party the embraces a supermajority of American Jews, Muslims, Atheists, Agnostics, Buddhists, Hindus and Wiccans, as well as many Christians, it has to have a big tent when it comes to religion. Even Orthdox Christians find it pretty hard to find acceptance on the red side of the fence and tend to turn to the Democrats. As a result, the Democratic party can not adorn its functions with religious trappings to any great extent and must adhere to a strong policy of separation of church and state to hold its coalition together.
This love hate relationship makes the question of how Democrats should reach out to Christianity a perennial topic of discussion in liberal circles. I am increasingly coming to the conclusion that this is not an issue that the non-Christian wing of the Democratic party can fruitfully address affirmatively. Simply put, non-evangelical Christianity is a little confused about its direction in life at the moment, which makes appealling to it difficult. The partisan divide in our country is playing out within every mainline denomination in the country. Gay rights is often the issue used to provoke the fights, but it the divisions run deeper to fundamental understandings about what the Christian endeavor means. The Presbyterians (USA), ELCA Lutherans and Episcopalians are all deeply enmeshed in the issue right now. The United Church of Christ has basically reached a point where the liberals have won. The Southern Baptist Convention has basically purged itself of moderates in the images of Jimmy Carter, Bill Clinton and Al Gore.
Until liberal and moderate Christianity can develop enough of a distinct public persona of its own to itself address the failings of the Christian Right, and until it is comfortable setting itself apart from them instead of feeling lumped in with them, there is very little that the Democratic party can do to resolve its love hate relationship other than advance the policies of economic and social justice which are at the Democratic party's core. Right now, moderate and liberal Christianity has no public persona, has no prominent leaders (and no, some committee chair chosen by the National Council of Churches doesn't count), and is struggling with its own identity. Mainline Christians both want to copy and want to define themselves against far more politically prominent evangelical Christianity. In the meantime, in the context of politics, Democrats seperate church and state, as individuals look for the party and church they are most comfortable with, rather than making their party a religious movement.