"It's great that the breast-feeding rates have gone up," said Shu, "but it's hard to know whether that improvement was because of the new policy or because the staff is now spending more time educating new moms about the benefits of breast-feeding."
For those who cannot breast-feed for medical or other reasons, formula is an "excellent alternative," she said.
"Low-income families who choose formula but are unable to afford it may end up feeding their babies unhealthy alternatives, such as water, juice or cow's milk," said Shu. "Having free samples available until these families can get on WIC [the Women, Infant and Children program] or otherwise find the finances for formula can save infant lives."
New York's Health and Hospitals Corp. said it would continue to make formula available for women who request it or are unable to breast-feed for medical reasons. Only 24 percent of the city's babies are discharged exclusively breast-feeding.
"From my perspective, that's a bogus argument," said Alan D. Aviles, head of the city's Health and Hospitals Corp., to The New York Times. "The reality is that there's nothing cheaper than feeding a child breast milk."
But in a society that provides little support for breast-feeding, the issue takes on larger political ramifications, according to Kim Gandy, president of the National Organization for Women.
"There is no question that breast-feeding is better for babies and actually has some benefits for mother as well, but we as a society make it very difficult — and removing free formula coupons from [a] postbirth swag bag doesn't address those barriers," said Gandy.
"It sends a good message, but it doesn't make other options easier or possible for women," she said.
Most companies still only grant women 12 weeks maternity leave — barely enough time for mother and baby to bond or to establish a good nursing regimen, according to Gandy.
More than 60 percent of mothers of young children work. Only a third of large companies provide a private, secure area where women can express breast milk during the workday and only 7 percent offer on-site or near-site child care, according to a 2005 national study of employers by the nonprofit Families and Work Institute.
"We are saying you're a bad mom if you don't breast-feed, but we are going to make it impossible for you," she said. "It's a big guilt trip with nothing at the end."
The debate rages on and mothers are caught in the middle.
Freelance writer Ronda Kaysen just gave birth to her first child in Mexico and has been fighting a different kind of social attitude.
"Here they pressure you to formula feed," said Kaysen. "Wealthy women bottle-feed and poor women breast-feed. My friend who is a college professor and plans to have children is horrified I am breast-feeding."
Kaysen struggled to prevent the Mexican maternity ward nurses from giving her baby boy sugar water or bottle formula. She even switched obstetricians to find one who would support her decision to breast-feed.
Still, she understands the complexity of the choice women have to make.
"I think it is a personal decision," said Kaysen. "To me it seems like the easiest thing to do. Bottle-feeding just seems like so much more work."