"Children and young adults with certain pre-existing medical conditions, and children, particularly younger children, should be included," said Dr. Andrew Pavia, chief of pediatric infectious disease at the University of Utah.
Others argued police, firefighters, the military, even utility workers, should also have priority.
"We don't want any of these people out in time of a national crisis," said Dr. Howard Markel at the University of Michigan.
Visit the ABC News OnCall+ Swine Flu Center to get all your questions answered.
Any flu virus can be dangerous for a pregnant woman, but swine flu appears to be especially threatening.
The flu can be particularly dangerous in the second and third trimester of pregnancy, both for mother and baby.
That was the case for Kelly Tunstall, who was eight months pregnant when she developed flu symptoms. Tunstall was put in a medically induced coma in the hopes it would save her and her baby. Both she and her newborn survived.
"I found out that I had the swine flu after I had woken up from the coma," Tunstall told "Good Morning America." "The first thing I did when I woke up was I put my hands on my stomach and asked where my baby was, and was told that she was delivered by C-section. I was terrified that I had lost her and I didn't have my baby."
"I want every pregnant woman to know that if they have any kind of flu symptoms, push the doctor for a test," she said. "And if the doctor won't test them, insist that they treat them like they have the swine flu."
Dr. Jacques Moritz, director of gynecology at New York's St.Luke's Roosevelt Hospital, said Tuesday that a pregnant woman's weakened immune system makes her especially susceptible to the virus.
"What the body does, and what the baby does, really, is it sends out a message, 'Don't get rid of me,'" Moritz said. "So it brings down the immune system, so you don't reject the fetus."
He added, "Anybody that is going to be pregnant, in the second or third trimester during this upcoming flu season, should get vaccinated before, obviously, the flu season."
But pregnant women may be reluctant to receive vaccines, especially brand-new ones, while they're expecting. Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases at the National Institutes of Health, said on Tuesday it's "understandable" that pregnant women are hesitant to get vaccinated.
"That's a natural reflex, but you have to understand the balance of the risk of a vaccination," Fauci added.
"Unfortunately, the flu vaccine has been recommended since 2004 for any woman that's going to be pregnant during flu season, and yet we know that less than 15 percent of actually get vaccinated," Jamieson said. "So we do need to do a better job of ensuring pregnant women are vaccinated against influenza, both seasonal influenza as well as pandemic influenza."
Dr. William Schaffner, chairman of Vanderbilt University Medical Center's department of preventive medicine, advised pregnant women today that "The first thing you do is get vaccinated against the regular influenza and then stay alert when H1N1 vaccine becomes available, and get vaccinated then if that's the recommendation at the time."