"I think at the moment, with 2.5 million doses, you are pretty vulnerable," warns professor John Oxford of the Royal London Hospital.
"The lack of advanced planning up until the moment in the United States, in the sense of not having a huge stockpile I think your citizens deserve, has surprised me and has dismayed me," he admits.
Faced with worldwide demand, the Roche company, which produces Tamiflu, has organized a first-come, first-served waiting list. The United States is nowhere near the top.
"The way we are approaching the discussions with governments is that we are operating on a first-come, first-serve basis," says Dr. David Reddy, head of the pandemic task force at Roche.
"Do we wish we had ordered it sooner and more of it? I suspect one could say yes," admits Leavitt. "Are we moving rapidly to assure that we have it? The answer is also yes."
When asked why the United States did not place its orders for Tamiflu sooner, Leavitt replied, "I can't answer that. I don't know the answer to that."
Even leading Republicans in Congress say the Bush administration has not handled the planning for a possible flu epidemic well.
Senate Majority Leader Bill Frist, R-Tenn., says the current Tamiflu stockpile of 2 million could spell disaster.
"That's totally inadequate. Totally inadequate today," says Frist, who is also a physician. "The Tamiflu is what people would go after. It's what you're going to ask for, I'm going to ask for, immediately."
Leavitt says deciding who gets the 2.5 million doses of Tamiflu currently on hand in the United States is part of the federal government's response plan. However, he also admits that thought has motivated the government to move rapidly in securing more doses of the medicine.
"It isn't going to happen tomorrow, but if it happened the day after that, we would not be in as good as a position as we will be in six months," he says.
However, in the end, even the country's top health officials concede that a killer flu epidemic this winter would make the scenes of Katrina pale in comparison.
"You know, I was down in New Orleans in that crowded airport now a couple weeks ago," Frist says. "And this could be not just equal to that, but many multiple times that. Hundreds of people laid out, all dying, because there was no therapy. And a lot of people don't realize for this avian flu virus, there will be very little effective therapy available early on."
ABC News' Rhonda Schwartz, Michael Bicks, Samantha Chapman, Maddy Sauer, Simon Surowicz, Jill Rackmill, Steve Baker, Monica DelaRosa and Jennifer Needleman contributed to this report.