"If it closes that clinic, then so be it," Bryant said during a bill signing ceremony in his Capitol office.
The law requires anyone performing abortions in an abortion facility to be an obstetrician-gynecologist with admitting privileges at a local hospital. Those privileges aren't easy for doctors to get, either because they live out of state or because some religious-affiliated hospitals might refuse to associate with people who perform elective abortions.
Diane Derzis, who runs the Jackson Women's Health Organization, disputes that such privileges are needed and says the requirements threaten the clinic's existence. She said her clinic already has an agreement that allows patients with complications to be transferred immediately to a local hospital.
Derzis recently said the doctors working at the clinic are OB-GYNs, but only one of the three had local hospital privileges. She said the clinic will try to comply with the new regulations, but if it can't, she'll file a lawsuit.
Robert McDuff, a Jackson attorney who has handled cases for abortion-rights supporters, said he believes the new law is flawed. Documents show that in 1996, a federal judge blocked a Mississippi law that would've required anyone doing abortions in an abortion facility to complete an OB-GYN residency.
"The United States Constitution prohibits states from forcing a woman who unintentionally becomes pregnant to bear a child against her will," McDuff said.
Terri Herring of Madison, national director of Pro Life America Network, was among a dozen people standing behind Bryant during Monday's ceremony, and he gave her one of the three pens he used to sign the bill.
"No woman leaves an abortion clinic uninjured," Herring said. "They may not go to the emergency room, but they bear the scars of an abortion for the rest of their life. Losing a child is a devastating event in any woman's life."
Bryant was elected governor last November and took office in January.
"Today you see the first step in a movement, I believe, to do what we campaigned on - to say we're going to try to end abortion in Mississippi," Bryant said after signing the bill.
However, it's not clear that the new law will accomplish that goal. Doctors who do fewer than 10 abortions a month, or fewer than 100 a year, aren't required to have their offices regulated as abortion facilities.
The Mississippi State Department of Health website shows 2,297 abortions, listed as "induced terminations," were performed in the state in 2010, the most recent year for which statistics were available. Of that number, 2,251 were performed on Mississippi residents. The site does not specify how many were done at the clinic and how many in other offices or hospitals.
Abortion-rights advocates say Mississippi is enacting a law that could be found unconstitutional under the framework of Roe v. Wade, the 1973 U.S. Supreme Court decision that established a nationwide right to abortion.
Those pushing the law defend its constitutionality and say admitting privileges are vital so doctors can continue to treat patients if complications arise from an abortion.
Mississippi already requires a 24-hour waiting period for an abortion and parental or judicial consent for any minor seeking the procedure. It's also among the few states where only a single clinic operates. North Dakota and South Dakota also each have one clinic.
Eight other states - Alabama, Arizona, Indiana, Kansas, Missouri, Oklahoma, South Carolina and Utah - require doctors who perform abortions to have admitting privileges in local hospitals, according to NARAL Pro-Choice America, an abortion-rights group. However, the Kansas law was blocked in 2011, first in federal court, then in state court.
The eight other states all have at least one clinic. Some of them enacted the requirement through legislation, while South Carolina did it through regulations set by its health department.