Giuliani has won over many hostile Republican constituencies by offering an implied bargain of federalism. He understands that "what works in New York doesn't necessarily work in Mississippi or Montana." In other words, he doesn't seek to dye the multihued American quilt New York blue.
On abortion, for example, Giuliani remains pro-choice, but he's signaled that he might be OK with "strict constructionist" judges overturning Roe vs. Wade and sending the issue back to the states. This isn't the pro-life ideal, but pro-lifers and even some conservative pro-choicers understand this would be enormous progress. And, if you believe even a fraction of the rhetoric we've heard for decades about how the GOP is held hostage by religious conservatives, it's hard not to salute Giuliani's courage.
Earlier in the campaign, he had a similarly base-displeasing position on guns. But Giuliani understood that such a view would have gotten booed by NRAers, who legitimately believe that gun rights are as real as free-speech rights and are far more grounded in the Constitution than abortion rights. (Gun rights have the No. 2 spot in the Bill of Rights, after all, while abortion rights merely exist in the fairyland of constitutional penumbrae).
Still, Giuliani could have argued that all sorts of rights can and should be regulated at the local level while still preserving constitutional protections. He could have given the NRA half a loaf by saying that he'd appoint judges who understand that the feds shouldn't be in the business of restricting explicit constitutional rights. And while the courts certainly aren't on his side on this point, they aren't with him on abortion either.
In a race filled with liberals and conservatives who want to impose a single vision on the country, the Giuliani federalist bargain has the most potential for expanding meaningful freedom and political diversity. It'll be a shame if the stevedore is willing to throw that over the side at the first hint of stormy weather.