Majikthise has a theologian in residence who contends that Democrats can and ought to appeal to Christian adherents on the basis of the progressivism of The New Testament and the teachings of Jesus.
I won't disagree that there isn't some room for Democrats to win over religiously-principled persons and to reframe the values debate in a manner that would reconcile the positions and advance the ideals of both.
But I'm less optimistic about this than I once was. The two basic problems I see are:
1) The evolution versus creation debate; and paradoxically,
2) Liberal assumptions about how "literally" most Christian conservatives take the Bible.
On the first point, the debate over our earth's and humanity's origins is what we might call a basic "worldview" conflict. In other words, this issue is likely to trump most others, and if Christians think (or are convinced by their religious elite) that Democrats are the "liberal" party, and that "liberals" essentially discount God's influence in creating us and sustaining the world (and are against "school prayer", the planting of religious monuments on government property, and other issues of highly symbolic, if lowly substantive value), then Christians are likely to discount anything else Democrats may put forward for a political agenda. In addition, Christians may justify to themselves their support of corporate appeasing Republican policies on a number of grounds so as to avoid ideological and mental "dissonance" or confusion in order to prioritize their basic worldview. Of the justifications Christians typically offer to minimize political support for more liberal economic policies are a) support for the poor should be carried out by individuals and churches and not the government; b) government programs are wasteful and ineffective (The "failure" of The War on Poverty, for example); c) blaming the poor themselves (personal responsibility); d) social programs are socialism-communism; e) more important to keep taxes low (so Christians can give more to charity, etc); and on and on.
As to point two, it's a paradox that the "strict constructivism" if you will, that Christians apply to Genesis and Exodus, and the belief that the Bible is infallible and should be understood literally, typically doesn't carry over to the New Testament where in most Christian churches, the essentials of Jesus's teachings simply don't get much attention. The Christian church of today is essentially a middle class phenomenon, concerned with its own and its members' prosperity. Strangely, while movies about Christ's death may sell in Evangelic-nation, movies about his ministry and teaching haven't. My basic point here is that most Christians are more likely to take their political cues from their pulpit than from the Bible. In other words, I'm afraid that the popular form of Christianity today is elite-driven and may not be suseptible to a "bottom up" revolution inspired by the followers in the pews.