Michele Goodwin, a law professor who specializes in health policy at the University of California, Irvine, said the standards for winning a request to stay a judicial order can be even higher than for an appeal. Fighting for one and losing it, she said, would raise particular risks of an appeals court decision that could take a similarly narrow view of what the C.D.C. may do in a public health crisis — and that, unlike a district court ruling, would also be a binding precedent.

“Losing sends a very strong message, and not just for the matter that happens to be at hand, but for other cases related to public health and safety,” she said.

The C.D.C. said on Wednesday that masking remained necessary to protect the public health of passengers on planes, trains, buses and subways, and a recent poll showed that 56 percent of Americans support the requirement. But airlines have called for an end to the requirement for months. And aside from public transportation, the administration has been deliberately moving away from masking as an essential pandemic tool for weeks.

Asked on April 11 why Mr. Biden wore a mask the previous weekend while Vice President Kamala Harris had stood over him maskless at an event, Jen Psaki, the White House press secretary, said it was up to each person to decide what to do.

“We all make decisions. Some people in here are wearing masks to make them more comfortable, or because they chose to that day,” she said, perhaps because they will be around family members or others who are particularly vulnerable. “And the president makes that decision, as we all do as well.”

In late February, the C.D.C. changed its guidelines in a way that made it far less likely that a county would be considered high risk, and specified that it recommended indoor mask-wearing in high-risk areas. In areas of moderate risk — like Manhattan and Washington, D.C. — those who are particularly vulnerable to severe illness from the virus should talk to their health care providers about whether to wear a mask, the revised rules say.

“Our emphasis right now is on getting people information and tools they need to make decisions for themselves,” Dr. Greta Massetti, a senior epidemiologist who is helping lead the agency’s pandemic response, said in an interview last week. Those choices should be “based on their own personal level of risk and their risk tolerance,” she said.

Sheryl Gay Stolberg and Katie Benner contributed reporting.