This month, one in five American I.C.U.s had reached or exceeded 95 percent of beds full. Alabama was one of the first states to run out, and the crisis is concentrated in the South, with small pockets of high occupancy elsewhere in the country. As cases and hospitalizations surged, the University of Tennessee Medical Center in Knoxville on Thursday requested assistance from the National Guard.

“I’ve never seen anything quite like it,” said Dr. Shannon Byrd, a pulmonologist in Knoxville, who described local hospitals filled to capacity, noting that the vast majority of I.C.U. patients in the region were unvaccinated. “It’s bringing whole families down and tearing families apart. They’re dying in droves and leaving surviving loved ones with a lot of funerals to go to.”

As in previous surges, hospitals have been forced to expand capacity by creating makeshift I.C.U.s in areas typically reserved for other types of care, and even in hallways or spare rooms. Experts say maintaining existing standards of care for the sickest patients may be difficult or impossible at hospitals with more than 95 percent I.C.U. occupancy.