I think it will hurt him. I don't think it will hurt his career, but certainly his chances for a presidential bid. People in this country, especially after the whole Clinton spiel, are more concerned about the personal lives of our politicians and whether their lives are conducted, in all aspects, to the conformity of a 'good moral and sincere person.' Comedy, especially of this type, doesn't play to well with the audience of this -mostly conservative- voting populace which I have described.

As someone that looks toward a person's ability to fulfill his/her office's position as well as their stances on certain issues, this would have absolutely no sway with me on whether I would vote for him or not. But unfortunately not all voters are this way. If they were, as alias claims, then Republicans wouldn't have to resign or lose substantial support (indeed from their own party) simply on the basis of them "coming out" and saying they're gay or revealing that they have 'cheated' or something of the sort (or getting caught).

So although this was just a joke and many people might have done such a thing for a laugh, and I'm sure it says nothing about the capability of Giuliani as a leader, there is the persona with the American voter (especially conservative base) that politicians should be above such things.

So, although it might not hurt his chances to win the general election all that much, it will certainly hurt his relationship with the Republican base, and it will definitely hurt his chances in the Republican primaries.