Andrew notes that Randall Terry of "Operation Rescue" fame says that "we must deny him the White House at all costs - even if it means Hillary becomes President." His analysis tracks mine:
As President Giuliani would be the de-facto head of the GOP; he would systematically destroy the political power of the pro-life movement within the GOP; he would pressure the party to take the pro-life plank out of the party platform; he would declare the "abortion issue" is divisive, and should not be part of federal races; he would make the GOP the mirror image of the DNC regarding child-killing, thus insuring that there is no pro-life party.
This seems about right to me. Giuliani's fine if you're just someone who deems abortion vaguely icky and wants it a bit more restricted, since judges he appoints will probably be fairly unfriendly to reproductive rights, but if you want a serious nationwide abortion ban you can't let the pro-life movement's control over the GOP slip away.