If Republicans try to claim they are the party of religion, family values, patriotism (really jingoism), defense, etc., try to beat them at their own game (as they defined it).
So, the DLC encourage Democrats "not to hide" their faith. And, when asked why Kerry lost the Presidential, Clinton pointed out that Obama had begun his Senatorial campaign with his pastor at his side. (Yes, we know how that turned out, but this was right after the 2004 election.) And, after Kerry lost he reportedly said something like "I got the religious thing wrong, didn't I?"
Obviously, Democrats can go only so far with religion, without bumping into anti-abortion and homophobia. But, apparently, they can bring their disciplines along for mixing church and state, semi-deifying the military, being "strong on defense," etc.
Meanwhile, increasing sanity on the issues of choice and equal rights has been prevailing throughout the nation, among both rank and file Republicans and rank and file Democrats, esp. in the younger demographics, though the war is far from won yet.
I am going to be interested to see what happens when those cease to be the lines in the sand between the parties as a whole.