And, Health and Human Services Secretary Kathleen Sebelius said, the government is hoping to have a vaccine for the new virus strain by the Fall.
Schieffer asked Homeland Security Secretary Janet Napolitano why the U.S. border with Mexico has not been closed since the H1N1 has become a concern.
"We relied on science and epidemiology," Napolitano said, "and the epidemiologists, the scientists say it would have done no good at all and come at enormous cost."
Instead, she said, her department has focused on the personal steps Americans can take.
"I don't think there has been over-reaction," to the H1N1 virus, she said. "We are having to make choices based on science."
"You may only get one shot at trying to limit the impact on health," Dr. Besser said. "As you learn more you are able to tailor your reaction."
"The main guidance is: if you are sick do not go to work," Dr. Besser said simply.
Secretary Sebelius said prior planning for pandemics has been especially helpful in guiding the new government. Sebelius was sworn into office only three days ago.
She said the government's approach to the viral strain has been "very appropriate."
Schieffer asked if there is any danger that the H1N1 virus could mutate into something more serious.
"Yes," Napolitano said. "The danger is it can come back in the Fall. It can come back in a more virulent form." She added that there is a significant amount of planning that the government and individuals must do over the summer.
Napolitano said that the virus has already become an international pandemic.
Dr. Besser said that there will likely be more deaths from the H1N1 virus, though these deaths would likely occur to people with underlying medical conditions.
"Influenza is a serious virus," he said, adding that it is "encouraging" that analysis of the virus does not indicate it to be similar to previous, more serious flu strains.
Sebelius said, "We are trying to guide people to the science," and recommended going to the CDC's Web site (www.cdc.gov) which is updated daily at 11 a.m.
More from Face The Nation (5.03.09):
To watch the CDC's Dr. Besser, Secretary Napolitano and Secretary Sebelius on Face The Nation click on the video player below.