I agree with everyone who says that James Dobson's threat to back a third party if Rudy Giuliani wins the Republican nomination on a pro-choice platform is mostly intended as an intervention in the primary. Dobson wants Giuliani to lose the nomination. Alternatively, he wants Giuliani to win the nomination only after shifting his position. But I don't think Dobdon's bluffing. Scott Lemieux thinks he is:
If push came to shove, though -- granting that a pro-choice Republican winning would be a disaster for the forced pregnancy minority -- I'm pretty sure that Dobson will not be indifferent about whether Giuliani or Clinton makes at least the next four years of federal judicial appointments.
To me that's backwards. The pro-life movement is going to act to safeguard its interests as a movement. Judges don't really matter to that. But if a Republican winning the White House on a pro-choice platform would be a crushing blow to the movement's power. The best thing is for a pro-life Republican to win the White House. But for a pro-choice Republican to win is worse than for a pro-choice Democrat to win, because it would undermine the narrative that abortion criminalization is a winning electoral issue for conservative politicians. If Rudy gets the nomination as a pro-choicer, I think Dobson et. al. have no choice but to try to throw the race to the Democrats, in order to make the argument that Republicans can only win if they run pro-life campaigns.