Hmm, they tried to do that in Texas recently, but Debra Medina only received around 20%. She played the role of a third party candidate in that aspect, but it was only in the primary. I would imagine that having a dual Republican party would hurt one or the other other, as Ben Franklin put it, "Divided We Fail." So yeah, it's an okay idea, but one that would hurt the candidates involved. If they had Tea Party and Traditional Republicans, it would be just like the divided and spineless Democrats in Congress...too divided to do anything to help. The worst aspect of it is that even if one or the other wins, eventually disagreeing would play a major role in slowing down the already slow Congress.