As Republicans come out of the Fox News, Glenn Beck, and Rush Limbaugh fog of propaganda, they have been discovering that America really doesn't like them very much. America has rejected the racism, misogyny, and greed that has become synonymous with Conservatism. While, I don't pretend to offer any advice to secular Republicans (if there are any), I do know how Conservative Christians can appeal to more people.
And that is simply to start living the teachings of Jesus Himself as expounded in the verses of the Bible that appear in Red (1Cor 2:1-5). Abortion existed well before the New Testament, but Jesus never mentioned it. Considering the time, the Centurion's "servant" was probably his gay lover, but Jesus never condemned him. When Paul preached to the Pagans on Mars hill, he didn't claim their religion bred terrorists.
The Good News of Christianity is not preached by picketing abortion clinics, it's not preached by collecting signatures to prevent gays from marrying. The Good News of Christianity is the person, life, and teaching of Jesus Christ of Nazareth, and Him crucified.