It was not even 9 in the morning and Dr. Sylvie de Souza’s green N95 mask, which was supposed to form a seal against her face, was already askew.

In freezing rain on Monday, she trudged in clogs between the emergency department she chairs at the Brooklyn Hospital Center and a tent outside, keeping a sharp eye on the trainee doctors, nurses and other staff members who would screen nearly 100 walk-in patients for the coronavirus that day.

Inside her E.R., more than a dozen people showing signs of infection waited for evaluation in an area used just a few weeks ago for stitches and casts. Another dozen lay on gurneys arranged one in front of the next, like a New York City car park. One man on a ventilator was waiting for space in the intensive care unit.

Minutes before paramedics wheeled in a heart attack patient, Dr. de Souza pointed to beds reserved for serious emergencies, separated by a newly constructed wall from the suspected virus cases. “This is our safe area,” she told a reporter. Then she corrected herself: “This is thought to be safe.” There was really no way to know.

The virus descended on the hospital three weeks ago. Dr. de Souza began writing down details of each potential case on a sheet of paper, a list that has grown to more than 800 patients, most of them seen in the walk-in tent.

She and others at the hospital had prepared for the growing onslaught: canceling most surgeries to bring down the census, designating an X-ray room just for patients suspected of having the virus, searching for supplies, barring most visitors, redeploying nurses to new roles, opening a hotline for the community.

The 175-year-old hospital — where Walt Whitman brought peaches and poems to comfort the Civil War wounded and where Anthony Fauci, the White House adviser who is now American’s most famous doctor, was born — is scaling up, as Gov. Andrew M. Cuomo has required all New York hospitals to do. The city, now the epicenter of the outbreak in the United States, had reported more than 20,000 confirmed infections and 280 deaths as of late Wednesday.

Licensed to treat 464 patients, the Brooklyn medical center typically has only enough staff and beds to handle 250 to 300. It is planning to increase that number by half if needed, but it may have to double it.

“I have so many different fears,” Dr. de Souza said on Wednesday. If the patient volume increases at the current pace, she is concerned the emergency room will be out of space by next week. If many patients are desperately ill and need life support, she worries about having to choose between them.

That morning for the first time, the health workers in the tent lifted their arms at a safe distance, as if they were holding hands, and said a prayer — to make the right decisions; to be protected, along with their patients, from the disease. Dr. de Souza plans to make it a tradition. “That’s all we can do: just pray, stick together, encourage each other, not get paralyzed by fear,” she said.

More than 40 percent of the hospital’s inpatients — scattered throughout the building — were confirmed or suspected coronavirus cases, as were more than two-thirds of the critical care patients. By Wednesday four had died, three of them since Monday.

More than a half-dozen hospital workers have contracted the virus and close to 50 staff members were potentially exposed by just one patient — the hospital’s first — who developed symptoms after being in the I.C.U. for a different medical problem, according to hospital leaders. Some of them have been in quarantine. Most worrisome, at the start of the week, two hospital staff members were receiving intensive care themselves. It feels, one employee said, like an invisible war.

In the emergency room on Monday, Dr. de Souza thought she saw a familiar face. A patient was coughing so hard he could barely speak. The young man was one of their own, Dr. Yijiao Fan, 31, an oral surgery resident with no prior medical issues who had tested positive for the virus. He had been in isolation at home all week and thought he was getting better, but began coughing blood that morning. He was awaiting a chest scan. He had no known risk factors other, perhaps, than practicing his profession.

Dr. Fan, as both surgeon and patient, had a message for a nation debating how to fight the pandemic. It was short enough to whisper between coughing fits: Just stay home.

‘This Is Where My Heart Is’

The hospital keeps personal protective equipment tightly guarded, because it is rapidly consuming donations of masks and other supplies; this week it was low on gowns. In the emergency room, those in the know approach the busy unit clerk, Donna Mosley, who is surrounded by ringing phones. “Hold on, I can do one thing at a time,” she told one employee.

Soon she bent down below her desk, fished in a box and handed over a set: an N95 mask that filters viruses; a surgical mask to go over it, with a plastic shield in crinkly packaging, donated by the relative of an emergency room doctor; a thin blue gown that covers a person’s front and arms and is open in back; and a pair of blue booties. Employees have to sign a form. One set per day.

The hospital has no parent company to request extra supplies from, no network of other institutions to share resources during the pandemic for the predominantly low-income and culturally diverse population it serves. It has resisted the era of mergers. “As an independent hospital we can control our destiny, control our resources, and really do what we think is right by the community,” said Gary G. Terrinoni, its president and chief executive.

Last week the hospital ran dangerously short of testing swabs, and its appeals for more reached the federal government. “We’re in disaster mode,” Mr. Terrinoni said.

The emergency room phone rang again. It was a man who lived down the street, offering handmade masks. “Are you selling them or donating them?” Dr. de Souza asked. Donating. She took his number and thanked him. The hospital has received gifts of gloves, food and a brown bottle with a mysterious liquid concocted by a local artisanal deodorant maker, which said it could be used to disinfect face shields. For now, that would be put aside.

An even bigger gift had arrived the previous night in a convoy of black sport utility vehicles that approached with flashing lights: boxes of coronavirus test kits reportedly from the federal strategic national stockpile, 200 in all. On Monday morning, two officers with the U.S. Public Health Service in crisp blue uniforms arrived to oversee their use.

But there was a problem. Test results from the kits would be delivered directly to the patient, not to the hospital. Dr. de Souza asked the public health officers how that could possibly work. “We can’t predict the patient’s clinical course,” she said. If someone was using a breathing tube, “they’re not going to be able to come to the phone and get their result.” Hospital leaders tried to sort out the issue, and the boxes of tests were not opened.

Under new restrictions from the local health department, communicated by fax to the hospital’s laboratory, doctors were supposed to test only the people sick enough to be admitted as inpatients. Dr. de Souza printed out the revised testing protocol, the eighth the hospital had received in recent weeks. She walked through the emergency department ripping down copies of the old one and stapling the new guidelines to the walls.

A few weeks ago, the hospital was able to send swabs to the city’s public health laboratory, which returned results in a day. Now, swabs were picked up by courier twice a day and sent to a Quest laboratory in California. At first the results took two days, then four days, and now it was a week.

“That’s really killing us,” Mr. Terrinoni said. On Wednesday the hospital had 65 patients awaiting results. They each had to be isolated in a room that was typically used for two patients.

The state had asked the hospital for a plan to increase bed capacity by 50 percent. Mr. Terrinoni found the space, but “we don’t have the beds, literally the physical beds, we don’t have the staffing.” The hospital put out a call to the city’s volunteer Medical Reserve Corps for doctors, nurses and respiratory therapists.

There were other important roles. Marilyn Hunt pushed a cart with a garbage can and supplies, stopping to change paper towels in one of the emergency department’s bathrooms. “We’re here in the front lines trying to do the best,” she said. “We’re supporting each other,” she added, “praying to God that this doesn’t do a lot of damage.”

After the virus hit, Dr. de Souza, 55, worked three weeks straight; her deputy was one of those quarantined for a while. Born in Paris, the daughter of a diplomat from Benin, and raised in several countries, Dr. de Souza trained at the Brooklyn hospital, located in Fort Greene. “This is where my heart is,” she said.

She offered to stay away from her family during the pandemic, but they insisted that she come home at night. When she arrives, she immediately takes a shower and washes her clothes in hot water. She sleeps in a separate room from her husband and maintains distance from him and their adult son and his girlfriend, who have moved in with them.

“Just trying to keep them safe, that’s my main concern,” she said. “I think every health care worker has the same concern.”

‘We All Probably Have It’

In the outdoor testing tent, Luciano Mahecha, 50, peeled off his ski jacket. A surgical intern placed a stethoscope on his back. “Your lungs are nice and clear. There’s no need to test,” Dr. Robert Jardine said. He told Mr. Mahecha to go home and stay there as long as his symptoms — a cough and fatigue — persisted.

Mr. Mahecha, whose first language is not English, agreed to keep away from other people, but he seemed to misunderstand whether he had the virus. “I thought I have it, but thank God everything is fine,” he said. “I don’t have it.”

“He probably has it,” Dr. Jardine told a reporter, and then gestured toward his colleagues. “We all probably have it. We’re exposed every day to people who we know” are more likely than others to be infected. Medical students were told to stop coming to the hospital last week, but residents like Dr. Jardine, less than a year out of medical school, accounted for a majority of the doctors evaluating people in the tent.

The rain picked up outside, and the floor began buckling. “We need help. Tent is getting flooded,” Dr. de Souza messaged the hospital’s engineers on the Signal app.

An older man shuffled into the tent, using a walker. He waited, sitting side by side with others coughing behind surgical masks they were given at the tent door. When he told the registrar he had come for wound care treatment, the staff member was alarmed. “You gotta get out of here!” he instructed.

Diana Purnell had a fever for a week, was short of breath and was sicker than most in the tent. Her age, 62, and high blood pressure put her at greater risk for complications from the coronavirus, which she suspected she had contracted from her Zumba teacher. She had called the New York State coronavirus hotline at 1 in the morning, waiting for two hours on hold until she woke up to a nurse’s voice.

Ms. Purnell said she was told a doctor would call her back about testing, but one never did. She said she reached out to an urgent care doctor in her neighborhood, but his clinic was closed.

In the emergency room, Ms. Purnell sat in a blue chair in the former fast track area with a dozen other listless patients, one of whom was missing a surgical mask and coughing. When she was taken for an X-ray, she was put on the side that was supposed to be kept for patients not suspected of having coronavirus infection: “She’s not Covid, so we can put her in this room,” a staff member said.

After the X-ray, Dr. Samridhi Sinha, a second-year resident, asked about her symptoms — fever, dry cough, extreme tiredness. “Yeah, it’s the virus,” the doctor said.

Aside from the test kits from the federal stockpile, still unopened in their boxes, the hospital was down to its last four testing swabs. They were being saved for critically ill inpatients. Dr. Sinha asked Ms. Purnell to go to a sink in the corner and spit into a cup typically used for urine samples. The health department did not recommend this method of coronavirus testing, but Quest was willing to accept it.

Because Ms. Purnell’s vital signs were stable and chest X-ray was clear, she was sent home to await a call from the health department if her test was positive. “If it’s not positive you’re not going to call?” she asked. Dr. Sinha said she didn’t think so. “Because we are testing thousands of people, right now only people who are testing positive are getting calls.”

‘It’s Going to Get Worse’

Walking through the emergency department, Dr. de Souza stopped to talk with two intensive care doctors.

“You’ve got one down here,” she told them. Amid the patients waiting to be moved upstairs was the critically ill patient on a ventilator.

The unit was full, Dr. Jose Orsini told her, adding, “And it’s going to get worse.”

Dr. de Souza dreads that possibility, haunted by accounts of Italian doctors denying lifesaving resources to older adults or providing inadequate care at overrun hospitals. “I’m asking myself if that’s where we’re going,” she said on Wednesday night. Some patients who were screened and went home have since returned with difficulty breathing, needing to be put on ventilators. “It’s getting really, really more difficult every day.”

The intensive care unit had 18 staffed beds, and it added six more Wednesday night. All are full and about two-thirds of the patients are confirmed or suspected to have coronavirus, according to Dr. James Gasperino, director of critical care services at the hospital.

He said eight more could be made immediately available in the surgical intensive care unit, and more still could be opened up, with additional staffing, in operating rooms, the surgical recovery area and a former intermediate care unit on a different floor.

Patients with the coronavirus who develop pneumonia can often require two to three weeks on a ventilator. “The intensity level is higher,” Dr. Gasperino said. “It’s harder to oxygenate than your typical flu patient who’s sick.” He added, “The staff is anxious.” So far none of the coronavirus patients requiring ventilators have recovered enough not to need one, although several younger patients were rapidly improving, he said.

Another patient, Dr. Gasperino said, went into cardiac arrest Sunday night, and he and his team were able to bring the person back to life. Four coronavirus patients at the hospital have died, including some whose families opted to withdraw life support.

This week the hospital counted up all the ventilators it had, including anesthesia machines used during surgeries. It found 61 in total. “We’re looking to purchase new ventilators,” Dr. Gasperino said. “We’re looking at one ventilator for two patients,” which some experts believe would be risky and difficult. He said they would need to simulate the process to make sure it worked.

While he hoped to avoid the worst-case scenario, Dr. Gasperino said he and the head of the ethics committee were planning to draft a guideline on how the hospital might ration ventilators, based on published recommendations.

On Tuesday — after 120 swabs from Quest arrived — Lenny Singletary, the hospital’s senior vice president for external affairs, returned the federal test swabs to the city’s department of emergency management, asking half-jokingly if he could trade them for ventilators.

The next day, he said the hospital accepted 12 ventilators from the emergency management office, St. George’s University and a company, Comprehensive Equipment Management Corporation.

For now, staff members are still pushing to do everything possible. “The hospital cannot close to other patients,” said Mr. Singletary, who grew up in the neighborhood. The medical center cares for children, women having babies, and people having strokes, among others. “You can’t shut down the hospital to treat coronavirus” alone, he said.

And so the staff members continue their work.

“They just take their courage in their hands,” Dr. de Souza said of her team. “They put on their garb and they show up. That’s what they do. Of course they have anxiety, of course they have fear, they’re human. None of us knows where this is taking us. We don’t even know if we might get sick. But none of them so far has defaulted on their duty, their calling.”