The high levels of burnout have exacerbated the staffing shortages, said Ethan Ruskin, a health educator at Kaiser Permanente in San Jose, Calif. Patients have to wait longer than usual for appointments, he said, only to face more delays in the waiting rooms.

“If they see something on your mammogram and send you for a sonogram, you’re going to be waiting weeks for a scan,” Mr. Ruskin said. “Meanwhile our sonographers have huge injury rates — things like stress fractures — because they are expected to see twice as many patients as they should.”

Mr. Ruskin, who works alongside doctors to educate patients about various diagnoses, such as diabetes, said employees in San Jose had been frustrated by their working conditions for more than three years. “The executives could stop the strike today, frankly,” Mr. Ruskin said. “To be clear, nobody wants to go out on strike. But we’re prepared to. We get into this field because we want to help people. We’re not sure what else to do at this point.”

Kaiser released a video and other resources in recent weeks to urge workers to push back on union calls for a strike. They argue that, in contrast to other high-profile labor negotiations, such as those among autoworkers and Hollywood actors, the effects of a health worker strike on the public would be immediate and life-threatening. The unions, however, have said that a strike is necessary to protect patient safety.

As the talks continue, the sides have yet to agree on a minimum hourly wage for workers and the rate of annual increases over the life of the four-year contract. The union wants a $25 hourly minimum wage and increases of 7 percent in the first two years and 6.25 percent in the two years afterward, according to its latest public proposal.

Kaiser has countered with minimum hourly wages of between $21 and $23 next year, increasing by a dollar a year. Raises would vary among locations, with workers in some places, like Northern California, receiving annual increases of 4 percent for four years, while some others would receive an increase of 3.5 percent the first year, followed by 3 percent annual increases.