Bedside is a series about health care from a nurse’s-eye view.

We nurses all have stories — if we’re lucky, it’s just one — about the time we failed a patient. It’s usually a problem of being too busy: too many cases, too many procedures to keep track of until one critical step, just one, slips through our frenetic fingers and someone gets hurt.

I saw it happen the first time while in nursing school. A patient needed an escalating dose of pain medicine. Her pain eased, but her breathing slowed and her oxygen level dropped. I told her nurse that the patient might need narcan, a reversing agent for opioids.

“Narcan?” The nurse didn’t have time for that. Caring for eight patients on a busy medical-surgery floor meant that getting through the day’s tasks took up all her time. Half an hour later, though, the patient needed an emergency team to revive her. I held her hand while an anesthesiologist stuck a tube down her throat. She ended up in intensive care.

It would be easy to blame the nurse. How could she be too busy? But she was a good nurse, smart and committed. She simply had too much to do, too many acute needs to address. And then one, just one, got out of control.

Bedside nurses are the hospital’s front line, but we can’t do the first-alert part of our jobs if there aren’t enough of us on the floor. More demands for paperwork, along with increasing complexity of care, means the amount of time any one nurse has for all her patients is diminishing. And as hospitals face increasing financial pressure, nurse staffing often takes a hit, because nurses make up the biggest portion of any hospital’s labor costs.

For patients, though, the moral calculus of the nurses-for-money exchange doesn’t add up. Pioneering work done by Linda H. Aiken at the University of Pennsylvania in 2002 showed that each extra patient a nurse had above an established nurse-patient ratio made it 7 percent more likely that one of the patients would die. She found that 20,000 people died a year because they were in hospitals with overworked nurses.

Research also shows that when floors are adequately staffed with bedside nurses, the number of patients injured by falls declines. Staff increases lead to decreases in hospital-acquired infections, which kill 100,000 patients every year.

The importance of sufficient nurse staffing is becoming irrefutable, so much so that the Registered Nurse Safe-Staffing Act of 2013 was recently introduced by Representatives Lois Capps, a Democrat from California and a nurse, and David Joyce, a Republican from Ohio.

Among other things, the act would require that hospitals include their nurse staffing levels on Medicare’s Hospital Compare Web site and post their staffing levels in a visible place in every hospital.

Concerns over money will determine whether this bill has even a chance at passing. It is collecting co-sponsors, but similar legislation has never gotten very far because hospital administrators view such mandates as too costly.

It’s hard to do a definitive cost-benefit analysis of a variable as complicated as nurse staffing because health care accounting systems are often byzantine. But data suggest that sufficient staffing can significantly reduce hospital costs.

Medicare penalizes hospitals for readmitting too many patients within 30 days of discharge, and a full nursing staff is one way to reduce readmissions. Having enough nurses increases patient-satisfaction scores, which also helps maintain Medicare reimbursement levels. Understaffing leads to burnout and nurses’ quitting their jobs, both of which cost money in terms of absenteeism and training new staff. Finally, falls and infections have associated costs.

What this discussion of finances misses, though, is that having enough nurses is not just about dollars and cents. It’s about limiting the suffering of human beings. When hospitals have insufficient nursing staffs, patients who would have gotten better can get hurt, or worse.

Several months ago I started a new job, and a few weeks in I heard my name being called. A patient getting a drug that can cause dangerous reactions was struggling to breathe. I hurried to her room, only to discover that I wasn’t needed. The other nurses from the floor were already there, stopping the infusion, checking the patient’s oxygen and drawing up the rescue medication.

The patient was rattled, but there were enough nurses to respond, and in the end she was completely fine.

Now picture the same events in a different hospital, one that doesn’t adequately staff, and this time the patient is you. As the drug drips in, you feel a malaise. You breathe deeply but can’t quite get enough air. Your thinking becomes confused, your heart races. Terrified, you press the call light, you yell for help, but the too few nurses on the floor are spread thin and no one comes to help in time. A routine infusion ends with a call to a rapid-response team, a stay in intensive care, intubation, ventilation, death.

This kind of breakdown is not the nurses’ fault, but the system’s. We are not an elastic resource. We can be where we are needed, but only if there are enough of us.

Theresa Brown is an oncology nurse and the author of “Critical Care: A New Nurse Faces Death, Life, and Everything in Between.”