That has parents worried - not just about the virus, but also about giving their kids yet another vaccine, as CBS News medical correspondent Dr. Jon LaPook reports.
Kori Buro is giving her daughters the usual childhood immunizations. But if a vaccine against the new form of H1N1 becomes available, her girls will not be in line.
"I don't want to have that kind of vaccination in my child yet until I know it's safe - 100 percent safe," Buro said.
A backlash against vaccines has picked up steam in recent years. A vocal minority fears vaccines can cause autism, despite consensus among experts that they don't. Now warnings are cropping up on the Web that the new H1N1 vaccine could be rushed to market without enough proof that it's safe.
"Are parents going to be given complete, truthful information about swine flu vaccine risks and have the right to say "yes" or "no" before their children are lined up and vaccination in the school setting?" Barbara Loe Fisher of the National Vaccine Information Center asked in a video on YouTube.
The concerns include possibly using chemical additives - or "adjuvants" - to boost the effectiveness of the vaccine. They have never been used in flu vaccines in the U.S., but have safely been used in others such as tetanus.
Critics also worry that some forms of the vaccine will contain thimerosol, a mercury-containing preservative.
"Thimerosol has never been associated in any valid scientific way with any adverse affect to the fetus or to young people," said Dr. William Schaffner of the Vanderbilt University Medical Center.
The government says a thimerosol-free vaccine will be available. But moms like Kori Buro still aren't sold.
"I don't feel just because the government is telling me to get this flu shot for her, or my youngest that I should go and do that," Buro said, indicating one of her children.
But, "You would be heart-broken if you did not vaccinate your child and that child got sick with influenza and found that your child was in the hospital close to death," Schaffner said.
The challenge for health officials - convincing the public to heed their advice, instead of a mother's intuition.