The regular flu kills between 46 and 88 children a year, according to Centers for Disease Control and Prevention data.
With H1N1 flu cases increasing throughout most of the country, more deaths are likely, Dr. Anne Schuchat said at a press conference Friday.
She noted that 37 states now are reporting widespread swine flu cases, up from 27 a week ago. A week ago, reports suggested that cases might be leveling off and even decreasing in some areas of the country, but that did not turn out to be an enduring national trend.
"We are seeing more illness, more hospitalizations, and more deaths," said Schuchat, who heads the CDC's National Center for Immunization and Respiratory Diseases.
Meanwhile, CDC officials say states have ordered 3.7 million doses of H1N1 flu vaccine for a campaign that started this week. Demand is exceeding supply, at least so far, and people seeking the vaccination can start by contacting their state or local health department to find out where to go, she said.
Intensive care units and emergency rooms are bracing for a long surge of flu patients, reports CBS News correspondent Mark Strassmann. States like Oklahoma want the vaccine and are waiting for answers.
Oklahomans are being urged to get it - by state health officials who complain the CDC can't tell them how much vaccine to expect, what type, or when, Strassmann reports.
"The vaccine supply distribution question, developing our plans for distributing vaccine, is very maddening," said Oklahoma epidemiologist Kristy Bradley.
Logistics are daunting. Oklahoma City's public schools have 37,000 kids - and only 31 nurses to give the vaccine, Strassmann reports. Another obstacle? Public resistance, despite reassurance from health officials the vaccine is safe.
"We just have to convince the people to bring their children to us," says Debby Johnson of Oklahoma City Public Schools.
Health officials also said more data is trickling in from several clinical trials of the new vaccine, and so far no serious side effects have been reported.
Preliminary information from one study indicates that both a seasonal flu shot and a H1N1 flu shot are effective when given during the same doctor's office visit. However, the government is not recommending that people get the nasal spray versions of the seasonal and H1N1 flu vaccines at the same time.
The nasal sprays contain weakened, live virus, and the government doesn't have data on how a person's immune system would react to exposure to both at the same time, said Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases.
The CDC doesn't have an exact count of all H1N1 flu deaths and hospitalizations, but existing reports suggest the infection has caused more than 600 deaths and more than 9,000 hospitalizations since it was first identified in April.
Read more at the CDC H1N1 Update Web site.