One patient had lymphoma and heart failure. Another was 85 years old with metastatic cancer. A third was 83 and had dementia and lung disease. All were critically ill with the coronavirus, and, a doctor said, all were hooked up to ventilators in recent weeks at a major Manhattan hospital.

But soon, patients such as those might not receive similar aggressive treatment. As people with the virus overwhelm New York City hospitals, doctors have stepped up pressure on state health officials to give them a rare and unsettling power: the right to withhold care from patients who are not likely to recover.

Dwindling supplies mean there might not be enough ventilators or other items for everyone, and many doctors say they are growing increasingly uneasy with treating every patient equally. They believe medical workers soon might need to make difficult choices about treatment.

“Usually, the standard is to intubate and do CPR and do all those things,” said Dr. Angela Mills, the chief of emergency medicine services at NewYork-Presbyterian/Columbia University Medical Center. “There’s no question about it; that will not most likely be sustainable.”