Whoever's feeding the press all the embarrassing Giuliani material -- the video of the 1989 speech in which he advocates public funding of abortions for poor women, the list of non-right-wing-friendly judicial appointees -- is doing a fine job. I bet it will hurt Giuliani.
However, I bet he'll still be leading in the GOP polls after it's all been absorbed. What I think would really hurt Rudy with Republican voters is evidence, if it exists and if a competing campaign can find it, of him being nice to, or saying nice things about, any of the usual wingnut antichrists -- Bill Clinton, Hillary Clinton, Al Gore, John Kerry, Ted Kennedy, Jimmy Carter, George Soros. Less potent but still useful would be evidence of his support for Mario Cuomo in 1993. Video of the endorsement is available, but if there was face-to-face Rudy-Mario bonhomie (I can't remember), that might hurt him with Republican voters, even though Cuomo dropped off the antichrist charts a long time ago.
This concerns the "tribal" part of what Matt Stoller calls "tribal authoritarianism" -- if voters in the base see Rudy not being true to the tribe, I think they're going to get angrier than they are at his deviations from the old litmus tests.