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Mrs. Shaver said she believed that in addition to Southwestern Women’s Options, the University of New Mexico Center for Reproductive Health, which advertises abortions up to 22 weeks, would have to change its practice.

But that depends on how pregnancies are measured.

The Albuquerque initiative sets the ban at 20 weeks from conception, but pregnancies often are measured by gestational age, or the first day of a woman’s last period, which is usually about two weeks before conception. According to the Charlotte Lozier Institute, most states that have enacted bans measure from fertilization but several do measure gestational age.

The women’s groups in Albuquerque say they have made headway with voters by questioning the way the referendum is written: It doesn’t include exceptions for rape or incest, and they said questions about the 20-week timeline also have troubled some voters.

The UNM Center didn’t return a message seeking comment about whether it would be affected.

Southwestern Women’s Options — the chief target of the referendum — referred calls to the state American Civil Liberties Union.

Twenty-week abortion bans enacted by state legislatures are being tested in courts, where the results have been mixed. A version of the ban passed the U.S. House this year and has been introduced in the Senate, but there is little chance the Democrat-led chamber will bring it to the floor.

The science also is contested. A growing amount of literature says fetuses may feel pain at 20 weeks, and pro-life advocates say that’s enough reason to extend protections to that level.

Pro-choice advocates say most science points to later in the pregnancy before a fetus could feel pain, and doctors say even if they can feel pain, there are ways to mitigate it during an abortion — including with anesthesia.

Pro-choice advocates also say women seeking abortions that late in pregnancy are usually the ones in crisis — they have discovered a severe abnormality or have some other complication that has pushed them to what all sides acknowledge is a wrenching decision.

“This is the last place the government should be,” Ms. Koob said.