Covid-19 hospitalizations in the United States hit an all-time high of 61,964 on Tuesday, as the raging pandemic continued to shatter record after record and strain medical facilities.

The number of people hospitalized with the coronavirus, tallied by the Covid Tracking Project, has more than doubled since September, and now exceeds the peak reached early in the pandemic, when 59,940 hospitalized patients were reported on April 15. A second peak in the summer fell just short of matching that record, with 59,718 hospitalizations on July 23.

Those spikes in April and July lasted only a few days and quickly subsided, but as winter approaches experts do not expect that this time. New cases are setting records in much of the United States, and rates of hospitalizations and deaths are following them upward.

The United States surpassed 10 million known cases on Sunday, and is averaging more than 111,000 new cases a day, a record.

While the number of patients continues to climb, a shortage of nurses and other medical personnel is limiting the ability to add more hospital beds to care for them.

The critical staff shortage, especially in Western states that struggle to attract doctors and other medical workers even in the best of times, is causing growing alarm, and driving some places to take extraordinary measures.

El Paso, a border city of 680,000, now has more people hospitalized with Covid-19 than most states — 1,076 as of Tuesday — and is more than doubling its supply of mobile morgues, to 10 from four.

The University Medical Center, a teaching hospital in El Paso, set up tents to care for patients in a parking lot. A downtown convention center became a field hospital, and the state began airlifting dozens of intensive care patients to other cities to free up more space.

Gov. Douglas J. Burgum of North Dakota, which has the worst infection and death rates per person in the country, announced on Monday that health care workers who have tested positive but have no symptoms could continue to work in hospitals and nursing homes under certain restrictions, including that they treat only Covid-19 patients.

The Centers for Disease Control and Prevention’s guidelines allow the use of asymptomatic personnel during severe staff shortages. Mr. Burgum said his state was about two or three weeks away from facing “severe constraints” in hospital capacity.

In Wisconsin, now among the hardest-hit states, a major health care provider, Aurora Health Care, announced it would pause testing sites in Sinai, Green Bay and Kenosha and focus on bedside care, a spokeswoman for the health care system said. Hospitalizations in the greater Milwaukee area have increased fivefold in the past two months.

When cases spiked in New York in April and in the South over the summer, health care professionals flew in from elsewhere to help. But now, officials describe a kind of national gridlock.

“Everywhere is either hard hit or is watching their Covid numbers go up, and are expecting to get a lot of flu patients,” said Nancy Foster, a vice president of the American Hospital Association. “The ability of health care professionals to pick up and leave their hometowns is very limited.”

That has left hospitals jockeying to find extra staff.

In Utah, for example, Intermountain Health Care, which runs some 22 hospitals, just added another 200 nurses, including 30 imported from New York. But Dr. Mark Briesacher, the company’s chief executive, said they were hard pressed to find more, a comment echoed by the heads of three other major medical groups in the state.

“We are at the tipping point,” Dr. Briesacher told a news conference on Monday. “We are beyond our normal capacity of caring for patients who are the most sick.”

Along the southern tier of neighboring Idaho, smaller hospitals have been told they can no longer rely on transfers to Utah of their most critical patients, said Toni Lawson, the vice president for governmental relations at the 40-member Idaho Hospital Association.

Even before the pandemic, the small rural hospitals in many Western states often depended on traveling nurses. But with Wyoming, Montana, the Dakotas and Utah all facing the same problem, the going rate for an I.C.U. nurse in the region has doubled to $120 an hour, more than small hospitals can afford, she said.

That leaves the small hospitals having to transfer some of their sickest patients to larger medical centers — and those beds are getting scarce, too, she said. “I do not want to say it is a crisis yet,” Ms. Lawson said, but if the system reaches capacity, “you start making difficult decisions of who gets what care.”

Although advances in coronavirus treatment have shortened hospital stays, the sheer number of patients is swamping hospitals.

Medical officials said they could try to fit in more Covid patients by stopping all but the most dire emergency surgery, or by recalling retired medical workers, but ultimately the only solution is fewer infections.

“The numbers across the board are troubling, but to address the hospital side of it, you have to address the public health side of it,” said David Dillon of the Missouri Hospital Association.

— Neil MacFarquhar and Nicholas Bogel-Burroughs The New York Times