CASCADE, Idaho — It was 3 a.m. at the 10-bed hospital near the River of No Return, and by every measure, Ella Wenrich should have been dead.Gastrointestinal bleeding had sent her hemoglobin level — typically above 12 — down to 3.3, and she needed an enormous blood transfusion at a larger medical center. But amid a surge in Covid cases, every major facility within 400 miles refused to take her. The smallest hospital in Idaho was, once again, on its own.The doctor woke the sheriff and sent him barreling north in his pickup truck with a cardboard box lined with ice packs and a mission to bring back blood. Ms. Wenrich, 83, known as Ms. Ella, needed seven units. The rush paid off and she survived. She worries the hospital that saved her may not.For 46 million Americans, rural hospitals are a lifeline, yet an increasing number of them are closing. The federal government is trying to resuscitate them with a new program that offers a huge infusion of cash to ease their financial strain. But it comes with a bewildering condition: They must end all inpatient care.The program, which invites more than 1,700 small institutions to become federally designated “rural emergency hospitals,” would inject monthly payments amounting to more than $3 million a year into each of their budgets, a game-changing total for many that would not only keep them open but allow them to expand services and staff. In return, they must commit to discharging or transferring their patients to bigger hospitals within 24 hours.The government’s reasoning is simple: Many rural hospitals can no longer afford to offer inpatient care. A rural closure is often preceded by a decline in volume, according to a congressional report, and empty beds can drain the hospital’s ability to provide outpatient services that the community needs.But the new opportunity is presenting many institutions with an excruciating choice.“On one hand, you have a massive incentive, a ‘Wow!’ kind of deal that feels impossible to turn down,” said Harold Miller, the president of the nonprofit Center for Healthcare Quality and Payment Reform. “But it’s based on this longstanding myth that they’ve been forced to deliver inpatient services — not that their communities need those services to survive.”Nurses at Cascade Medical Center vacuum, clean toilets and scrub down the blood-splattered emergency room after each trauma patient. A father walks his daughter and wife into the emergency room at dusk following a sledding accident. Tight on space, Cascade Medical Center converted an ambulance bay into a CT imaging suite.Medical staff members organize supplies in a patient room used for storage.Some rural health care providers and health policy analysts say the officials behind the rule are out of touch with the difficulties of transferring rural patients. Bigger hospitals — bogged down with Covid surges, pediatric R.S.V. patients and their own financial woes — are increasingly unwilling to accept transferred patients, particularly from small field hospitals unaffiliated with their own systems.There are also blizzards, downed cattle fences and mountain pass roads that close for months at a time.“I really want to give this policy a chance to work well,” said Katy Kozhimannil, director of the University of Minnesota Rural Health Research Center. But gambling with transfers could mean that “some of the most extremely remote and marginalized communities could end up with no care at all — and that’s what we were trying to avoid in the first place.”Over 180 rural hospitals have closed in the United States since 2005, according to a recent analysis, with a record 19 closings in 2020 alone. Then, the trend seemed to pivot toward a brighter future: In 2021, the number plummeted to just two.“The total margins look great, but behind them, there’s a sad reality,” said Carrie Cochran-McClain, the chief policy officer of the National Rural Health Association. More than $15 billion in pandemic-era federal aid was injected into rural hospitals to keep them open. On Dec. 31, most of it will expire.Now, labor expenses per patient are up more than a third, and payment rates are lagging. Over 600 rural hospitals — 30 percent of the total — are at risk of shuttering. More than 200 could close within three years, according to a study by the Center for Healthcare Quality and Payment Reform. In 10 states, at least 40 percent of rural hospitals are in danger: In Kansas, 16 could close within three years; in Mississippi, 24.When rural hospitals close, it is medically and economically devastating for communities. They have supported one in every 12 rural jobs and contributed to about $220 billion in economic activity per year, according to the American Hospital Association. A community’s population typically shrinks soon thereafter.A Covid test was transported to an improvised laboratory in the parking lot of Cascade Medical Center. Tight on space, the staff has turned to shipping containers.Shelby Hallan, a registered nurse, worked with Alison Zeller, a physical therapist, to help patient Jack Sides stand up in his room at Cascade.Tom Reinhardt, the chief executive at Cascade, had previously led the much larger St. Alphonsus Neighborhood Hospital just outside Boise. After he broke his leg hiking and sought care in Cascade, he wanted to join the team.The new federal program is designed to mitigate that threat. Struggling hospitals that convert themselves to rural emergency hospitals will receive monthly payments of $272,866, with increases based on inflation each year. They will also receive higher Medicare reimbursements than larger hospitals.The new option takes effect on Jan. 1.A spokeswoman for the Centers for Medicare and Medicaid Services said that the “prohibition” on inpatient services was set by Congress in an appropriations act for 2021 and that the agency’s role was “to enforce such requirements.”During the mandatory comment period, members of the public suggested exceptions for labor and delivery patients; the agency responded: “Since this is a statutory requirement we do not have the ability to make exceptions.”The office of Senator Charles E. Grassley, Republican of Iowa, who is one of the lawmakers behind the program, said in a November statement, “The goal is to preserve patient access to emergency medical care in rural areas that can no longer support a fully operational inpatient hospital.”Cascade Medical Center, where Ms. Wenrich was treated, seems like exactly the type of hospital that federal officials had in mind.This former lumber mill community is home to less than a thousand people, but the hospital serves patients from across 2,800 square miles; patients travel up to eight hours round trip from homes without addresses. “About 12 miles past Yellow Pine,” one said; “middle fork of the Salmon River — can’t get there by road,” another described.Here, where deer graze on a helipad and nurses ventilate patients by hand, resourcefulness has long been the drumbeat of the operation. The 11,000-square-foot center houses an emergency room, lab and radiology unit, and primary care clinic, as well as sections for mental health counseling and physical therapy. Space is so tight, the staff keeps the CT scanner in the ambulance garage. Doctors treat patients in a shipping container in the driveway.Because of budget constraints at the hospital, which is open day and night, every day of the year, there are just two physicians, who trade shifts. A cardiologist and a podiatrist visit once a month; radiology technologists rotate in for a week at a time. The nurses vacuum the hallways, clean the toilets and scrub down the blood-splattered emergency room after each trauma patient. The staff eats family-style lunches off a single sheet pan.“We play eight-man football with a nine-person roster,” said Tom Reinhardt, the hospital’s chief executive, who smiles widely and often pauses midsentence to readdress his listener by name.Shane Cusic and Chad Kreider, both nurses, folded laundry during the night shift at Cascade.Like many small rural hospitals, Cascade Medical Center’s future seems uncertain. Significant federal funds are available if the hospital decides to shift away from inpatient care.In central Idaho, the rural town of Cascade has a median age that is 20 years higher than the state’s. Residents are often admitted for chronic conditions like congestive heart failure.Mr. Reinhardt had previously led the much larger St. Alphonsus Neighborhood Hospital just outside Boise. After he broke his leg hiking and sought care in Cascade, he told his wife to let him know when she was ready to retire from the city. He wanted to join the team.“It’s the neatest job I’ve ever had,” he said. “And we do have an IT department,” he joked. “His name is Craig.”Small rural facilities like Cascade don’t enjoy revenue from lucrative procedures like heart and joint surgeries, which medical systems often capitalize on to increase cash flow. The hospital is operating at a loss of around 20 percent for the third year in a row.If Cascade Medical Center were to become a rural emergency hospital, it would lose payments from both inpatients and swing beds — the total was more than $624,000 in 2021 — and services those patients would have used, such as lab tests and X-rays. But for a hospital with a total revenue of just $7.3 million in 2021, the new $3.2 million annual payments could still put it significantly ahead. That could allow it to offer colonoscopies, cataract surgeries and other services that many residents go without.“The math gets harder and harder,” Mr. Reinhardt said. “It would be irresponsible for me to not take this option to the board.”But in rural towns like Cascade, general inpatient services are at the core of the community’s needs. Residents are routinely admitted for chronic conditions like congestive heart failure; others need rehabilitation after accidents before they can return to isolated houses to live on their own.Ashley Thompson, 70, was admitted overnight with a pulmonary embolism before he could be transferred to a specialist in Boise. Ron Wise, 78, who came on a recent morning to get a flu shot from the nurse, Bradi (who is his granddaughter), has repeatedly received inpatient care for heart failure and came in once for internal bleeding after he fell off the roof of his barn.“If it weren’t for the good Lord and this hospital, I wouldn’t be here — clear as that,” he said.Dan Rosbrugh spent five days at Cascade Medical Center recovering from pancreatitis. If the hospital ended inpatient care and larger ones in Boise were full, residents like Mr. Rosbrugh and his wife, Lynn, would have to go out of state for care.This former lumber mill community is home to less than a thousand people, but the hospital serves patients from across 2,800 square miles. Here, dozens of deer often linger in the parking lot and on the helipad.Dr. Katie Camarata, the physician who cared for Ella Wenrich, in one of the few inpatient rooms at Cascade Medical Center.Michael Hanson for The New York TimesEven intensive-care patients who belong in special units are dependent on Cascade. One recent diabetic ketoacidosis patient was kept alive at Cascade because the Life Flight helicopter from Boise couldn’t navigate through thick fog. Another patient, who was having a heart attack, was denied a transfer to Saint Luke’s in Boise because Cascade is not part of the hospital’s system, but doctors treated her successfully at Cascade.During Covid surges, Dr. Katie Camarata, the physician who cared for Ms. Wenrich, stayed up overnight with critically ill patients, calling hospital systems in surrounding states. All seven refused the transfers. Eventually, the Cascade staff created their own negative-pressure rooms so it could keep highly infectious patients in-house without infecting others.Providing inpatient care “comes down to a moral decision,” said Dan Rosbrugh, 75, who was admitted to Cascade in October with pancreatitis pain he called “worse than my broken leg in Vietnam.” He stayed for five days. When he could eat again, his doctor, Dr. Ron Ellsworth, drove to the D9 Grocery to buy him pudding.Some hospitals have already made the decision to accept the government’s offer. St. Margaret’s Health in Illinois told community members that it would convert one of its two hospitals, which are less than four miles apart, into a rural emergency one but keep the other full service. Sturgis Hospital in Michigan was struggling to operate on a loan when it learned of the new designation and said it would convert.Others plan to forgo it. Chief executives at Ouachita County Medical Center in Camden, Ark.; Southern Inyo Hospital in Lone Pine, Calif.; and Comanche County Hospital in Coldwater, Kan., said that ending inpatient services would be untenable for their elderly populations.Tim Reeves, the chief executive of the 16-bed Bucktail Medical Center in Renovo, Pa., ruled out conversion because, in the case of another pandemic surge, there would be “nowhere to transfer my patients anymore.”In 2021, Bucktail’s financial margin for patient services was negative 43 percent.“Am I going to lose some revenue? Possibly,” he said. “But is it more important to provide the services needed? That’s the position we’re taking.”In Cascade, the decision doesn’t seem so simple. Perhaps a hospital without inpatient services is better than no hospital at all.After Ms. Wenrich’s husband died suddenly, she broke her ankle and then came down with pneumonia. Ms. Wenrich is legally blind, and there is no nursing home or assisted living in the county. It was the Cascade staff that came to her tiny trailer home to transport her — 42 miles, through the canyon fog, across Rainbow Bridge and into the CT scanner in the ambulance garage to check her lungs for fluid.She stayed there for almost a week.The hospital is open day and night, every day of the year, but there are just two physicians who trade shifts.