NEW YORK --Dr. Sarah Miller was visibly shaken despite her jovial tone as she recounted how "it can happen on a date, or anywhere, really," that people "out of nowhere" become aggressive and judgmental when learning what some of her medical duties entail.

"I mean, what would you say to someone calling you a murderer?" asked Miller, a New York City-based family doctor who runs her own medical practice as well as providing abortion care services at Planned Parenthood centers in New York.

"Abortion care is not a controversial subject. And I know I'm saying that when there is controversy surrounding it," she said.

Pro-life protesters outside a New York City Planned Parenthood clinic. CBS News

The abortion debate in America is one that inflames passions on both sides, but doctors like Miller told CBS News that, from their point of view, it's about providing safe medical procedures in line with guaranteed legal rights.

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On Wednesday, the Supreme Court heard oral arguments in Whole Woman's Health v. Hellerstedt, a case challenging a restrictive Texas law. If the court upholds the law, it would make abortions harder or impossible to obtain for many women and could reduce the number of clinics in Texas (a state with a female population of about 13 million) to as few as 10 by requiring doctors who perform abortions to obtain admitting privileges at nearby hospitals.

It would also require clinics, including many Planned Parenthood centers, to meet the standards of ambulatory surgical centers.

"The discrepancy between the medical reality and the political reality has caused so many problems," said Miller. "Abortions are one of the safest procedures. Safe and legal abortions have one of the lowest complication risks of any procedure."

Abortion rights advocates argue that recent Texas laws present the most serious threat to abortion rights in decades and that they will "unquestionably" impact the most vulnerable women.

Dr. Sarah Miller. CBS News

More than 100 other women have filed several supporting briefs to the Supreme Court abortion case describing how their abortions enabled them to control their bodies and plan for the future.

Meanwhile, an anti-abortion-rights group, the Justice Foundation, filed a brief on behalf of more than 3,000 women who say they suffered psychological or physical harm from their abortions.

While Miller described her job as being "harder and harder" to do because of restrictive laws, she said she remained "hopeful" about the Supreme Court case.

"I don't think there's room politically for someone's value systems to be forced on anyone else," said Miller. "If we're meant to feel like we are doing something wrong or we're ashamed for the decisions that we make, then we're not going to be able to speak out about the normalcy of it."

Planned Parenthood, a nonprofit that provides reproductive health services to both men and women, is a key target for the anti-abortion-rights movement because of the organization's size and national reach.

Many equate Planned Parenthood facilities with abortion clinics, but abortions actually make up a small portion of the services they provide. In the New York City Planned Parenthood clinics where Miller works, just under 18,000 abortions were provided in 2015.

The November attack by self-proclaimed gunman Robert Dear on a Planned Parenthood facility in Colorado Springs, Colorado, served as a stark reminder of how volatile the abortion debate can become.

Dear is charged with multiple counts of murder and attempted murder for the five-hour siege in which three people were killed.

CBS News reported last September that an FBI intelligence bulletin went out to law enforcement agencies nationwide warning of threats to reproductive health facilities.

During the summer, the release of secretly recorded, edited videos by The Center for Medical Progress, purporting to show Planned Parenthood employees discussing the harvesting and selling of fetal tissue, which is illegal, has stoked controversy about the organization.

Planned Parenthood has denied any wrongdoing, and two people who infiltrated the organization and shot the videos face criminal charges in Texas.

However, the allegations have fueled calls to defund Planned Parenthood, and the organization has been a hot-button issue on the presidential campaign trail. Most Republican presidential candidates have vehemently opposed Planned Parenthood. In turn, Democrats have claimed the Republicans are waging a "war on women" and are attempting to undo the Supreme Court's 1973 Roe v. Wade ruling recognizing abortion rights.

"There is no Planned Parenthood that uses funding from the federal government to fund their abortion services," said Miller on a recent winter morning in New York City's newest Planned Parenthood facility, in the borough of Queens.

"The funding we're talking about cutting off to Planned Parenthood is the funding that will get people the cancer prevention, the infection treatment and testing and the essential primary care services that we've all needed in our lives."

Asked about her reaction to the Colorado Springs shooting, Miller said, "The anger or the disappointment is more geared toward people who fuel those types of actions than this one particular sick and sad man."

She added that she considers "repeated anti-abortion rhetoric" and legal attacks on Planned Parenthood more worrisome.

One week later, on a cold and sunny Saturday morning on Manhattan's Bleecker Street, a group of about two dozen protesters gathered across the street of a Planned Parenthood facility.

"They're here rain or shine every first Saturday," Carrie Mumah, a spokesperson for Planned Parenthood, told CBS News that morning as protesters prayed silently between singing religious songs. A handful of anti-abortion-rights bikers approached passing couples with leaflets.

"I feel as if this country was based on life, liberty and the pursuit of happiness -- the first thing being life," one protester, who described himself as an abortion "survivor," told CBS News.

Asked whether laws were to blame for the relatively small number of willing abortion care providers and doctors, especially in states like Texas, Miller said inadequate medical training was also at fault.

"How can we provide services that we aren't trained to do?" she asked.

The American College of Obstetricians and Gynecologists recommends that all medical schools offer abortion training, but many don't. In a 2005 survey of U.S. medical schools, the most recent comprehensive one of its kind, only 32 percent said they offered lectures about abortion as part of an OB-GYN rotation. Twenty-three percent reported "no formal education" about abortion whatsoever, and more than half -- 55 percent -- reported that they offered no clinical exposure to abortion to their students.

A survey six years later revealed that 89 percent of all U.S. counties lacked an abortion clinic -- and 38 percent of women live in those counties.

"Women suffer as a result of these policies. If they get worse, the hardships will get worse, the barriers will get worse," said Miller. "Three in 10 women will have an abortion by the time they're 45."

"Pregnancy will not disappear, and abortions will not disappear," she said.