Already, abortion providers say, long drives and packed waiting rooms have become the norm, and second-trimester abortions have become more common because of the wait for an appointment.

Tenesha Duncan, an administrator at Southwestern Women’s Surgery Center in Dallas, said her clinic’s patient load had doubled since the new law took effect, with more patients coming from rural parts of the state and also from Houston and Austin. Demand is so high that the clinic has expanded its procedure hours to 60 from 40 a week, Ms. Duncan said, and has assigned seven employees to answer phones.

Candice Russell, a 32-year-old administrative assistant from Irving, was 12 weeks along when she learned she was pregnant in 2014, she said, and she faced a wait of two and a half weeks for an abortion in Dallas or Fort Worth.

Instead, Ms. Russell took out a high-interest payday loan and flew to California, where her partner lived and where she was able to get an abortion in a matter of days.

“That’s what floored me — they could see me on this day or this day or this day,” she said. “It put me into this downward financial spiral that lasted a couple of months, but compared to a lot of people, I’m super privileged. I know there are tons of people that will be affected by these closures, and they’re never going to be able to fly to California.”

Volunteers for the Texas Equal Access Fund, one of several groups in Texas that help women pay for abortions, said that because of the longer wait for appointments, the fund was fielding far more requests for assistance from women in their second trimester of pregnancy than it used to.