Some 20,000 workers are already waiting in hotels, staging areas, and — for those employed locally — in their homes to be called into action once conditions are safe enough, said Neil Nissan, a spokesman for Duke Energy, which has 4 million customers in the Carolinas. And those are just the workers assigned to assist Duke, the largest power company in the Carolinas, said Brian Reil, a spokesman for Edison Electric Institute, an industry group that helps coordinate the mutual aid response. An additional 20,000 workers have been dispatched to other utilities in the area, he said.

Computer modeling indicates that somewhere between one to three million of Duke Energy’s customers will lose power, some for brief periods and others for weeks because of coastal flooding, Mr. Nissan said.

For those reasons, Mr. Nissan said, Duke has been telling its customers that the storm is “a potentially life-changing event.”

Puerto Rico did not immediately invoke mutual aid after Hurricane Maria because the governor said the island did not have aid agreements in place and he believed that the island did not have enough money set aside for initial payments that might be owed to mainland utilities. That decision made the hurricane the only known case in recent history in which mutual aid was not invoked after a major power failure.

But instead of working with Puerto Rico to invoke the aid and deal with any costs later, FEMA took the extraordinary step of asking the United States Army Corps of Engineers to take a leading part in the emergency restoration, a task it had never carried out before.

Puerto Rico compounded the mistake by hiring a small contractor, Whitefish Energy, to carry out many of the tasks that thousands of mutual aid workers would have undertaken under normal circumstances. And the logistics of moving people, equipment and millions of parts to the island helped bog down the effort until it became a slow, frustrating and ultimately disastrous effort to restore power to desperate citizens.

This time, FEMA officials say they are prepared, though they are striking more cautious tones than the president and emphasizing the destructive power of the hurricane.