The conservative National Review and others on the right have voiced serious doubts about (or outright opposition to) Rudy Giuliani, who is now clearly in the 2008 presidential race, owing in part to his too accommodating stance on gay unions and abortion. In fact, Rudy's position (supports civil unions but opposes same-sex marriage; opposes a federal amendment against same-sex marriage) is the same as Hillary's and Obama's. But more significantly, Rudy would be the first GOP presidential nominee who has marched in Pride parades, addressed Log Cabin events, criticized "don't ask, don't tell" and, in an Odd Couple twist, moved in with two gay guys (a long-term couple) after his divorce. (Southern Voice has a nice wrap-up on all the leading candidates' positions.)
But I doubt that will stop the Human Rights Campaign, now essentially the gay lobby of the Democratic Party, from endorsing their gal sometime during the primary season (in 2000, they endorsed Gore before it was clear whether the GOP candidate would be Bush or, in a possible upset, McCain). If/when they do so, their message to the GOP could be summarized as: "You could nominate the ghost of Harvey Milk and we'd still be loyal Democrats. So don't even bother trying to reach out to us. After all, we favor securing patronage positions for our key activists in a Clinton adminstration much more than we care about moderating anti-gay views in the other party."