"What do Republicans have to do to become relevant again?"
Rep. is a dead party. However, not for most of the reasons listed here. They don't actually believe what they say. They talk a big game about less taxes, small government, but when they're in power, they're basically democrats with a negative media image. If they 'truely' want to get back into power, they need to quit acting like Democrat Lite, nominate some real conservatives that talk the game, and live it when in office. Quit pandering to the other sides base, and focus on their own.