“He coughed on me last night when I hugged him,” she said. “I don’t feel scared. I never was scared.”

Dr. Luciana Borio, a former chief scientist at the Food and Drug Administration who advised Mr. Biden during the transition, said reaching the unvaccinated was now arguably “the hardest aspect” of the U.S. response — one that would require a change of course in federal and state priorities, such as reopening community vaccine sites or urging providers to put more focus back on first doses.

A spokeswoman for the Department of Health and Human Services pointed to a wide-ranging vaccine public education campaign still underway at the agency, with special attention now to reaching young children and those in need of a booster. New ads this week targeting rural, younger Americans featured the language: “When you’re done with Covid, it doesn’t mean it’s done with you.” Other ads targeting rural adults warned of the financial costs of contracting the virus.

In Cleveland, the Covid picture is one of the bleakest in the country. Intensive care units are crammed with patients with the Delta variant, with a surge of new Omicron infections looming. New infections in Cuyahoga County, which includes Cleveland, have grown by 234 percent in the past two weeks.

Ohio, where 60 percent of people have gotten at least one shot, now has the country’s highest rate of Covid-19 hospitalization, and doctors say emergency rooms and I.C.U.s are running out of beds. They are being forced to call people in from holiday vacations as growing breakthrough infections whittle away at their staff levels.

There was just a single open bed in a sixth-floor intensive care unit at the main campus of the Cleveland Clinic on Thursday morning, where about 90 percent of I.C.U. patients were unvaccinated. The demand for intensive care has gotten so great that when a bed opens up, nurses are cleaning rooms and moving patients themselves to make space for the next patient.

“It feels like it will never end,” said Claire Strauser, a nurse manager in the intensive care unit whose adult son still has refused her entreaties to get vaccinated. Ms. Strauser said she will probably not see him over Christmas to reduce her own chances of getting infected and sidelined from a job she is devoted to.

“I don’t know what can change,” she said. “They’re just dug in.”