You can't just "infiltrate" a church and get votes for a politician. Just as a good segment of America is over politicians, a good segment of the Christian church is over the political manipulation of the right.
That being said, I think that the church (at least the protestant evangelical wing) has experienced a change in values over the past few years, with many more people getting serious about social justice issues, caring for the poor, and speaking up for the vulnerable. Many, many more Christians have become involved in things like caring for orphans overseas, domestic foster care, community outreach, refugee organizations, etc. Having been very involved in these myself, the issues with American political status quo--the way that the wars create vulnerable women and orphans, the ways that the failed War on Drugs has put thousands of kids into the system, and the ways that crony capitalism exploits people economically are very evident. These people are ripe for the pickings--are are mostly a younger (25-40) audience influenced not only at church but by bloggers and online communities.
The challenge: there seems to be a prevalent attitude among these same Christians that politics is worthless. I know many people who are the most socially active and serving in their community that never vote. There is a general disgust for "Religious Right" Christians, as they are largely viewed as hypocrites.