The Democratic National Committee Thursday cited that fact to argue that Giuliani did not do enough to protect firefighters and other workers at the site.
"The more Americans learn more about Rudy Giuliani's poor decision-making after 9/11 and his role in this tragedy, the more they will question his ability to lead the country," said Karen Finney, a spokeswoman for the Democratic National Committee, though the woman who died did not work on the rescue operations.
The Giuliani campaign also pointed out that the former mayor did mandate that Ground Zero workers wear respirators, a point confirmed by city reports filed in the months after 9/11.
"I don't think it's right to blame Rudy Giuliani for what's going on here," Joe Lhota, former New York Deputy Mayor for Operations said on MSNBC last week. "What I think we need to focus on are the people who did work there, who did come down here to work with the rescue effort and the cleanup effort, that we take care of them now."
One strategist for a rival campaign said the other Republicans in the race have an incentive to highlight areas where Giuliani's 9/11 record is less than stellar, though he acknowledged that all candidates have to proceed carefully given Giuliani's wide popularity.
"People don't know much about him outside of 9/11, but over the last couple of weeks and moving forward they're going to become better acquainted with his record," said the strategist, who spoke on condition of anonymity. "He doesn't have much other than this to run on."
Fred Siegel, a Giuliani biographer and a senior fellow at the Manhattan Institute's Center for Civic Innovation, said he sees an early parallel between the current attacks on Giuliani and the withering campaign organized against Kerry in 2004 by the Swift Boat Veterans for Truth.
But Siegel added that Giuliani is so well known by the public that it may be impossible for rival campaigns to tar him as an ineffective leader, even if some of the critiques have some validity.
"This is potentially damaging, but I wouldn't overplay it. People saw for themselves what happened, and it's very hard to counteract that," Siegel said. "People have their own experience with how he handled 9/11, and their own experiences visiting New York, and that will make it much harder to 'Swift Boat' him."
Siegel said he views some of the attacks on Giuliani's record as unfair.
He called it "bizarre," for instance, to suggest that Giuliani wasn't focusing on terrorism before 9/11, since he was emphasizing emergency preparedness throughout his tenure as mayor.
Still, his decision to put the emergency command center in the World Trade Center -- which had previously been the target of a terrorist attack, in 1993 -- certainly proved to be an instance where his judgment was "less than acute," Siegel said.
Asked about that decision last weekend on Fox News, Giuliani blamed Hauer, who was then his emergency management director.
"He recommended that site as the site that would be the best site. It was largely on his recommendation that that site was selected," Giuliani said.
But Hauer sharply disputes that account.
"That's Rudy's own reality that he lives in," he told The New York Times this week. "It is not, in fact, the truth."