Well, of course they can. But should they? Of that, I am much less sure and this essay doesn't go any distance toward convincing me. Kyle-Anne Shiver suggests that, in fact, the President doesn't have all that much to do with the question of abortion, save his role in nominating judges who are likely to overturn Roe v. Wade (she says "strict constructionist") and dealing at the margins with some abortion legislation. I'm not sure that's right - or at least it's incomplete.
The President has some control, for instance, over our aid budgets - one of the things that just makes the pro-abortion crowd hopping mad is how successive Republican administrations have tied American foreign aid up in ways that prevents it from expanding "reproductive rights." If Giuliani is President, do you think he'll continue the current administration's policy in that area? Why would he?
More importantly, Shiver herself recognizes that the President will have the opportunity to decide whether to veto bills funding abortions or embryonic stem-cell research (actually, she doesn't mention the latter), but, as she notes, Giuliani hasn't committed to vetoing those bills. Indeed, it's hard to see why he would - in his incarnation as Mayor, he was in favor of public funding of even the most grotesque forms of abortion procedures. If he's as hard-headed as she says, will he change his mind on this as well?
And, finally, there's something she just misses here. Suppose, now, that the Supreme Court one day overrules Roe v. Wade. (It's unlikely to happen in one fell swoop, but stick with me). The debates then turn to the legislatures - both federal and state. On the federal level, Congress can mandate that the states allow abortion merely by saying that they have to in order to keep their health-care funding. Would a President Giuliani veto such legislation? Color me doubtful. Perhaps more importantly, at the national level, having a pro-choice President will matter in those debates. The Presidency is the single most important bully pulpit in the nation and if he's firmly in the pro-choice camp, he's likely to sway things his way.
So this pro-lifer ain't convinced and Giuliani still isn't on my list of possibles...