(CNN) -- With her 5-week-old daughter crying in a bathroom at Nordstrom, and not knowing how to get the baby to latch on to her breast, Garima Nahar found herself surrounded by other women. Some offered tips, but one woman told the new mother to cover up or turn the other way.

"I had to kind of hide my tears and just be brave in front of her, because, you know what, 'I have a crying baby and I don't want to deal with you right now,' " said Nahar, a software manager in Chicago, Illinois.

Women across America have felt uncomfortable in public situations when breastfeeding their children. Sarah Hood of Fayetteville, Arkansas, who works in advertising, got stares when breastfeeding her son in the open.

Working mothers like Nahar and Hood have had to carefully tailor their schedules so that they can pump milk in the middle of the day, and avoid stares when they put bottles in the communal refrigerators. Some have to use a bathroom stall to pump milk, as there is no other space available.

Nursing mothers will now get additional support, thanks to page 1239 of the health care bill that President Obama recently signed into law. It requires employers to provide "a place, other than a bathroom, that is shielded from view and free from intrusion from co-workers and the public, which may be used by an employee to express breast milk." Only companies with less than 50 employees can claim it's an undue hardship.

"It reflects both a shifting attitude, a shifting reality, and also the impact of research that shows that it's healthier for the kids, and therefore good for the company, good for the family," said Ellen Galinsky, president and co-founder of the nonprofit research organization Families and Work Institute.

A recent study in the journal Pediatrics showed breastfeeding a child for the first six months of life would save nearly 1,000 lives and billions of dollars each year. That's because breastfeeding reduces the risk of certain illnesses such as pneumonia, according to the study. Much of the cost comes from excess premature deaths, the study authors said.

Read more about the study

Major medical and health organizations agree that breast milk by itself is sufficient for newborns and infants until they are 6 months old. But a 2009 report from the Centers for Disease Control and Prevention found that while 74 percent of women start breastfeeding, only 33 percent of mothers relied on breastfeeding only at three months. At six months, the numbers go down to 14 percent.

"There really is a lack of support for breastfeeding moms, and you see that in the statistics of breastfeeding rates," said Andi Silverman, mother of two sons and author of "Mama Knows Breast: A Beginner's Guide to Breastfeeding."

Attitudes toward breastfeeding generated copious discussion in social media circles when in December 2008 Facebook came under fire for taking down photos of mothers nursing babies. Thousands of users held a virtual protest and petitioned the social networking giant to allow breastfeeding photos.

"It's such a sad thing that our society looks at this as disgusting or weird," said Julie Dye of Boulder, Colorado, who was involved in that campaign.

At the same time, Dye herself has never personally had a bad experience breastfeeding in public.

"I will breastfeed anywhere, at almost any time. However I try not to be in your face," she said. "It does take some confidence -- you just have to know that it's the right thing for your child."

But some view the enthusiasm for breastfeeding as hysteria. Hanna Rosin, contributing editor at the Atlantic, isn't convinced that the medical benefits of breastfeeding are more than modest, and denounces the message that failing to breastfeed is irresponsible. Rosin wrote this piece in the Atlantic detailing her views.

The pressure to breastfeed is still tremendous: One woman with breast cancer recently wrote to Rosin that she is embarrassed to give her child a bottle, she said. And Cheryl Rosenberg of Orange County, California, says she experienced "nasty looks" when mixing formula in public for her first two children, who had rare allergies to breast milk.

"If you nurse for only a little while, there's definitely an indictment on it," said Rosenberg, who is a blogger and part of Silicon Valley Moms Group along with Nahar and Hood. "It's a lot of pressure to breastfeed from others in society, and yet the society as a whole doesn't support it."

Still, Rosenberg is enjoying breastfeeding her third child. Rosin agrees with others that it's "a lovely, natural part of mothering," but doesn't like the pressure. Rosin herself breastfed her first two children and, as she wrote in her article, decided on breastfeeding her third child only part time. She's also in favor of the provision about breastfeeding spaces in the health care law.

It's easy to see how moms might give up on breastfeeding if they go back to work, said Renata Matos of Kansas City, Missouri, who breastfed her son while working as a local government auditor. Carrying the pump around, making sure that the milk gets to the baby, and finding time to pump all are challenges with a full-time job, she said. Traveling is also a hassle: It always took Matos longer to go through airport security with her pump and milk.

About 49 percent of companies have some kind of space for nursing mothers to express milk, Galinsky said. In companies with 100 employees or more, it's 53 percent; in 1998, it was 37 percent.

The part of the law addressing breastfeeding spaces is "a win for the family and a win for the company -- they have less absenteeism, and the children are healthier," Galinsky said.

Not everyone is so enthusiastic. The Texas Association of Business calls it "inappropriate," saying the relationship between the employer and employee should be handled privately, not through a mandate from the federal government. Most employers do make accommodations, and this law will create additional expenses, he said.

"At a time when the economy is suffering, adding costs to employers means fewer employees," Hammond said.

Twenty-four states also have workplace-related legislation about breastfeeding. Read about the laws here.

A breastfeeding room doesn't have to be fancy, but should have a table, chair and outlet for plug-in pumps, said Dr. Melissa Bartick of Harvard Medical School and Massachusetts Breastfeeding Coalition. There should also be easy access to a refrigerator and a sink.

"The notion that if you have a baby or are nursing you should stay at home -- it's just a historical notion these days," Galinsky said.