I haven’t thought it all through yet, but it strikes me that a good place to begin is Terry Mattingly’s post at Get Religion. Mattingly points also to this Beliefnet piece by Steve Waldman, whose conclusions are worth noting:

To cement the gains with religious voters and Catholics, the Democrats will likely need to develop a more moderate position on abortion. These new pro-life Democrats will surely press the case; it’s an open question how the pro-choice Democrats who will still dominate the party will react.

Thanks to the Iraq war, Democrats now have an opening to win over more religious voters. However, the Iraq war won’t dominate forever and Democrats will now need to prove themselves worthy of centrist religious voters by altering their views on some social issues and dispelling the image that they’re hostile to faith.

I’m sure I’ll have more thoughts as I get the chance to look more closely at the data and at what the Democrats do.

I remain convinced that an early test, which President Bush can perhaps force by announcing that he’ll sign it if it crosses his desk, is the Democrats for Life’s
Pregnant Women Support Act, which is a classic pro-life Catholic/blue dog Democrat supported bill that needs more Republican co-sponsors. Supporting and, I hope, passing this bill would offer an example of principled bipartisanship. It’s absolutely the best thing pro-life folks can hope to get from the 109th or 110th Congresses. And it’s good politics, both for the message it sends about bipartisan cooperation and about the challenge it poses to the new Speaker about her commitment to both bipartisanship and a big tent Democratic party. She can’t be permitted any sort of fig leaf here.

Update: This article by the WaPo’s Alan Cooperman is disappointingly unilluminating. While we learn, for example, that Democrats won a marginally larger share of the white evangelical vote in 2006 than in 2004 and that Catholics swung to the Democrats this time, Cooperman says nothing about the relatively religiously conservative Democrats who won election. In a year where they faced a party that seemed intellectually and ideologically exhausted, saddled with an unpopular war, Democrats are not so religiously radioactive that some people would rather slit their wrists than vote for someone with a "D" next to his or her name.

I don’t think that Democrats should be too confident that the strategy they employed this year will work every time. Sooner or later, those morally conservative religious voters will ask themselves whether they’re really getting or going to get anything of substance from the party to which they lent their support this year.