It's interesting that in a country where religion is so tied with politics, people would still be strongly adherent to the First Amendment that a political party could be sunk if they so much as put the term "Christian" in its name.
If a Baptist tried to start a Christian Democratic party here, he'd get few votes from Methodists, Presbyterians, Episcopalians, or Catholics as they'd suspect he thought that he was a better Christian than they. Same for the other creeds. The multiplicity of Christian denominations makes it hard to form a Christian themed party here.