"I don't think we should be hysterical, but I don't think we should be complacent, either, because just the fact that we are safer does not mean we are completely safe and the job is done," Chertoff said in a speech at the National Press Club in Washington.
He warned against adopting what he called a "Sept. 10th mindset" that presumes "it really isn't possible to imagine a very serious successful attack on American soil."
Chertoff recommended a middle ground.
"I think we need to put ourselves right in the middle of the hysteria and complacency," he said.
The threats are evolving, he said, and the United States must adapt or be "doomed to fail."
Chertoff said there are many examples of how the nation is safer than it was before the deadly attacks by Muslim extremists engineered by the still-at-large Osama bin Laden. The Department of Homeland Security, he said, has "dramatically increased our ability to block dangerous people from coming into this country."
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