The 33-year-old Texas woman drove alone four hours through the night to get to the Louisiana abortion clinic for a consultation. She initially planned to sleep in her car, but an advocacy group helped arrange a hotel room.

Single and with three children ranging from 5 to 13, she worried that adding a baby now would take time, food, money and space away from her three children. She doesn’t have a job, and without help from groups offering a safe abortion, she said, she probably would have sought another way...