The company said it was not yet possible to tell individual customers when their service would be restored.

“We know how uncomfortable it is to be out of power,” said Eric Silagy, the company’s chief executive, at a news conference. “We get it. We have families here as well.”

The most serious consequences of the outages appeared to be unfolding at hospitals and nursing homes. As of Monday evening, 54 hospitals were operating on backup generators, according to data reported to the Florida Department of Health.

Some nursing homes in Florida reported they had been running on generators for more than a day, some going without air conditioning, others without power altogether as generators failed. Some of the state’s assisted living facilities, which also house people who rely on electricity-dependent medical equipment, had no backup generators and reported being completely without power on Monday.

Gail’s Assisted Living Facility in Tampa had been without power for nearly a day and had no backup generator, Gail Coleman, who runs the facility, said on Monday afternoon. One of her eight residents requires breathing treatments, and most have dementia.

“I don’t think they really know what’s going on,” she said. But most were seniors, and she feared for their safety in the unrelenting heat. “I just want them to get it turned back on. It’s frustrating.”

The state requires nursing homes to have plans to maintain power and to evacuate when necessary in emergencies, but some experts said the state had done little to enforce the rules or penalize nursing homes that did not follow their emergency plans in previous years.

For Monika and Vernon Maitland, of Cape Coral, Fla., Irma delivered more than an inconvenience. Mr. Maitland, 91, suffered a stroke last year that paralyzed half of his body, and Ms. Maitland, 70, worried he would develop painful bed sores without air conditioning to cool him down. She would have to try to keep him in a chair.

Florida was also feeling the loss of power on the road, where many traffic signals were out, turning every intersection into a four-way muddle. Drivers edged guardedly into multilane intersections with no guidance on when to go.

At a Mobil gas station off the turnpike in Palm City, the clerk pressed a calculator into service after the outage knocked out his cash register. A search and rescue team heading to the Keys was waiting for the bathroom, each person at the front of the line cracking the door open with a foot so the person inside was not forced to use the toilet in total darkness.