In Baltimore, resident Ivette Brown expressed her frustration with the system.
"We've been turned away. We were told they don't have anything," Brown told ABC News. "My children's health is at stake."
Kathleen Sebelius, secretary of the Department of Health and Human Services, said the vaccine is coming off the production lines slower than the administration would like, but that there will eventually be enough vaccine for everyone.
"We're pushing it out the door as fast as we can," Sebelius told "Good Morning America's" Diane Sawyer today. "There's a frustration that we have that the manufacturers are feeling. ... We just want people to be a little patient. It will be there. They will have one."
The government had initially said 40 million doses would be available by this time, but in reality, only one-fourth -- about 11 million -- of those are out. About 150 million doses will be needed to cover all Americans. Sebelius said the administration has ordered 250 million doses, with 16.5 million doses expected to be out the door by today.
The first outbreak of the H1N1, more commonly known as swine flu, was reported in April, and the first vaccines were made available in October. Sebelius disagreed with the idea that it's too late to get vaccinated, and that more doses are on their way.
"We've got 150,000 sites around the country. We would urge people to be a little patient," Sebelius said. "I hope that people aren't discouraged, and I know that it's frustrating to wait in line, particularly if you end up with no vaccine and we wish this could've been smoother."
"We knew that it would come in waves, and the waves have been a bit slower but talk to you local health officials, get on the web site, get information on the local level and come back," Sebelius added.
On Saturday, President Obama declared the H1N1 virus a public health emergency, paving the way for hospitals to create off-site wards to treat those infected with the virus. But while it gives health facilities and doctors flexibility in how they deal with swine flu patients, the declaration does nothing to speed up the production of vaccines. In fact, it may have inadvertently created some panic as facilities around the country saw long lines and not enough doses to treat everyone.
A key issue is that the United States has to rely on vaccine manufacturing plants based in other countries to deliver the vaccine. Sebelius said investments are being made at the federal level to produce more vaccines and an additional plant is slated to start operations next year.
"It certainly is a concern. We rely on other nations to purchase the vaccine," Sebelius said. "Just as recently as 2004, there were only two vaccine manufacturers in the world, so we really have seen a growth in capacity. ... It's just the production capacity is scattered around the world with one here in U.S."
That is likely to bring little comfort to those waiting in line for hours to get the vaccine or doctors inundated with patients.
In Los Angeles county, one of the biggest fronts in the battle against the flu, 20,000 doses were given just on Saturday, but vaccines couldn't come fast enough.
"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."