Would such a party, drawing 10 percent of the population at most, concentrated almost entirely in the Old South, doom the rump Republicans?
Consider the 2000 election. Al Gore campaigned hard in Madison, Wisconsin at the tail end of the election in an effort to blunt the Naderites. In 1948, in contrast, Truman won a resounding victory despite the defection of the Dixiecrats and the Wallace Progressives. Why was that? As a border-state culturally conservative social democrat, he was able to portray the Democrats as Roosevelt’s national party. By naming Joe Lieberman as his running mate, Gore gestured in the direction of making the Democrats the national party. But there was something about Gore’s cultural profile that undermined this effort.
What if the rump Republicans recast themselves as the national party? For example, though the party would be divided between pro-abortion and anti-abortion factions, it would be united around the principle of local democracy. It’s easy to imagine many of the rebels being drawn back into the fold over time, and it’s easy to see how such a party, having jettisoned elements that repel voters outside of the South, could do reasonably well.
I think Reihan's absolutely right that Gore could have turned Nader's run to his advantage; I'm less convinced that Giuliani could do the same with a pro-life challenger, if only because the Republican brand is at such a low ebb right now that there are more severe limits on the next GOP nominee's ability to win over independents than there were on either Truman in '48 or Gore in 2000. But this doesn't mean that an attempted third-party challenger would doom Giuliani: As Matt says, the infrastructure social conservatives say they need for such a run is unlikely to materialize, which in turn means that you'd need a candidate with at least a certain amount of star power (at least as much as, well, Ralph Nader) to make voters pay any attention at all - and I really don't have a clue who that candidate would be. Rick Santorum isn't walking through that door ...
All this is complicated, of course, by the possibility of a Ron Paul third-party run, which would give conservatives a staunchly pro-life alternative in the race, but perhaps not of the sort that Richard Land and James Dobson are dreaming of.