Listen to this Christian couple's story (12 min).
Listen to the story of this married Christian couple, Danielle and Robb. They had gone through several miscarriages and one successful pregnancy brought to term. Then with this baby, Danielle's amniotic sac broke early, at about 22 weeks, and she was hospitalized. The diagnosis: the loss of amniotic fluid would cause the fetus severe limb deformities and underdeveloped lungs. Danielle would probably miscarry before the fetus reached a viable gestational age; and even if it did reach viability, it had almost a zero chance of any life at all once born. Danielle and Robb talked the situation over with their doctors and their consciences, and they decided to seek an abortion.
The problem: they're in Nebraska, where a woman can't get an abortion after a fetal heartbeat can be detected, unless the her life is immediately at risk.
In other words, the only way Danielle could have gotten a legal abortion would be to wait until she developed a deadly pregnancy complication, such as the leaking amniotic sac letting in some contagion that caused a massive septic infection that threatened to kill her.  Instead, the state of Nebraska forced the fetus to go through a week of increasing pregnancy complications and fetal deformities until the Danielle finally went into premature labor, and the baby died within minutes of birth. A nurse made the mother watch the newborn struggle to breathe before it finally died, so that the state could have the time of death.
This is what happens to ordinary people when abortions are banned. Because Danielle and Robb had a toddler at home, they couldn't just up and travel to another state to get the procedure done. Instead, Danielle was forced to a week of bed rest and then days of physical recovery from childbirth, along with the emotional trauma of being compelled to watch her deformed baby die for the convenience of the medical staff's recordkeeping. If she had been able to get the healthcare she needed, she could have been back to work and caring for her toddler within a few days.
Where is the state's interest in having the situation end this way?
 Coincidentally, premature rupture of the membranes is why my OB induced my labor a few days before my actual due date. It's a relatively common complication of late pregnancy. My OB's rule of thumb was to induce if labor hadn't started spontaneously within 24 hours of the rupture, because the rupture can provide a pathway for serious infection, as it's basically an open sore into the body.