"We knew it was limited and we kind of braced ourselves, but still you're never prepared to wait four hours in the car," resident Christina Deal told ABC News.
The county's health department said 3,000 doctors ordered the medicine, but only 400 have received it.
"I think the problem has been manufacturers were overly optimistic, and it's made planning much more difficult," Dr. Jonathan Fielding, director of the county's public health department, told ABC News. "There's nothing like a shortage to make people very concerned. ... It [swine flu] is not entirely predictable, and I think that's given rise to a lot of fears."
Chicago saw a similar scene. Seven clinics in that city used every drop they had and still ended up turning people away.
"If we had more supply, we could give it to more people, but we don't," said Dr. Terry Mason, Chicago health commissioner.
Forty-six states are reporting H1N1 as widespread, with more than 1,000 deaths and 20,000 hospitalizations. While some doctors say the seasonal flu is more dangerous than this new strain, the swine flu is different in that it affects young, even seemingly healthy people. About 30 percent of deaths have so far been in healthy people with no underlying problems.
Administration officials say getting vaccinated is the best defense against H1N1, and that people need to be patient and come back when more doses are available.
"I never like to see people inconvenienced. ... If we had found the vaccine earlier, we could have started a little earlier," Sebelius said on "GMA." "I think that getting vaccinated, even if you've had the flu in the summer or early fall, our scientists tell us that's a good plan."