"We're learning the recklessness with which ground zero was run, and Rudy Giuliani was the king of ground zero," Barrett said. "If this is the rationale for the candidacy of the leading candidate for president, it's about time that this is getting examined."
The firefighters' chief complaint is that Giuliani's rush to clean up ground zero prevented the remains of scores of firefighters from ever being recovered.
That complaint is legitimate, Siegel said, but has to be weighed against Giuliani's understandable desire to move as quickly as possible in clearing the wreckage from the World Trade Center site.
The key for the former mayor will be how he handles the questions that are being raised -- whether he takes it in stride and defends his record, or whether he loses his temper with those who are criticizing him, Siegel said.
"In a way, it might not be bad for Giuliani, in the sense that it's already out there and it's early," he said. "If he mishandles it, it can rise to that level of harming his campaign. If he doesn't handle it well, we'll know he can't handle the White House."
For his part, Giuliani has mostly brushed aside criticism of his record, saying he'd rather look forward than back.
"The best way to proceed there is we don't blame anybody; what we try to do is learn from it," candidate Giuliani said last month in Iowa.