I'm not so sure they will, in the long run. There have been a lot of snide comments about the "Christian Right" in the last few days from they typical liberal pundits and some politicians. This denigration of people who are only looking for justice and compassion will not hold them in great stead by those voters the Democrats believe they can woo by 'saying the right words' about religious topics, even though they won't be changing their ideas one whit!
I believe there are enough decent people left in America that this incident very well may mark the end of the Democrats' ability to pull the votes of any religious people at all.