"When my first son was born in 1969, they banned visitors except for immediate family because of the Asian flu epidemic," said Dr. Michelle Warren, medical director of the Center for Menopause, Hormonal Disorders, and Women's Health at New York Presbyterian Hospital.
And while the restrictions may not be popular, some are in place at hospitals even when influenza is not perceived to be as great a threat.
"Throughout the year, no matter if it's flu season or any time of the year, we do have some restrictions in our NICU and our birth center area," said Heying.
Those restrictions include monitoring visitors for illness and making everyone wash their hands.
"Obviously, we're always trying to protect our babies," said Heying. "Everyone would be required to wash their hands before they entered the [NICU]."
Many hospitals also restrict who can enter the NICU, because of the premature and other vulnerable newborns there, restrictions which can include children under 18.
At issue with some is how new mothers and their families will react to a ban of child visitors.
Green said that at Concord Hospital, reaction has been varied, with some mothers understanding and many upset.
"It's mixed; obviously it's not something under ideal circumstances we'd like to do," he said. "Many mothers today have a birth plan, and that birth plan has roles for the siblings of the newborn, and so the policy does interfere."
ABC News asked a number of physicians what they would expect the reaction to be, and got similarly mixed answers.
"I am certain that many families will react negatively to this prohibition, especially if there is no such recommendation by the CDC or other national or professional organization," said Dr. Manuel Porto, professor and chairman of the department of obstetrics and gynecology at the University of California-Irvine.
Other doctors were more optimistic.
"If they understand the reasons, I think they will be glad for the concern about safety," said Dr. Jerome Yankowitz, an obstetrician at the University of Iowa.
"The H1N1 flu is hitting us hard in the southeastern U.S.A. I think people would understand," said Dr. Kevin Ault, an associate professor of gynecology and obstetrics, at the Emory School of Medicine in Atlanta.
He also recommended vaccinations for the mother and people who will be around the baby, since children that young cannot receive the vaccine.
Dr. Jeff Ecker, an obstetrician who deals with high-risk deliveries at Massachusetts General Hospital, said such drastic steps are meaningless if the family does not follow through with them afterward, keeping the new baby away from sick visitors.
"Banning visitors absent symptoms seems both unnecessary and unpopular," he said. "Most babies room in with mothers and will soon be exposed to their family and visitors when they leave the hospital for home. Whether at home or in the hospital, the important issue is to avoid those most likely to be infectious as defined by symptoms."
Green noted that there has been one unexpected result for some new mothers that the hospital had not counted on.
"Since we've instituted the policy, mothers have reported to us that [they're] getting more rest," he said. "So that's an interesting unintended consequence."
Alessandra Sozio contributed to this report.