The bus bridges created winding lines and widespread gridlock, resulting from a simple math problem, Mr. Prendergast said: Between 1,500 and 2,000 people can pile into a train. A bus can fit no more than 75 or so.

Accordingly, connecting the boroughs by subway was the next priority. Late Friday, as the power returned, officials were confident they could restore full service to some trains, like the Lexington Avenue line and the No. 7, almost immediately. By Saturday morning, they had, and several other connections between boroughs followed.

After a news conference Saturday with Mr. Cuomo, Mr. Lhota held up a sheet of paper with a bar graph, depicting how much subway service had returned. By day’s end, it was expected to be 80 percent.

There were some hiccups. At West Fourth Street, unexpected third-rail and switch problems delayed the return of the D, F and M trains. As the authority prepared to bring the G train back this week, a transformer blew, keeping the train offline for the morning rush hour on Wednesday. There were still service gaps on the N train, the A train in Far Rockaway and the R line, among others.

On Thursday morning, inside his office, Mr. Lhota checked his BlackBerry often, hoping for an update on the L train. Moments later, he placed a call to Howard B. Glaser, Mr. Cuomo’s director of state operations, whom he wanted to brief on the Queens-Midtown Tunnel.

The tunnel could open Friday, he told Mr. Glaser, remarking that Mr. Bloomberg, “like an idiot,” had predicted publicly that the tunnel might open over the weekend. “He’s making it up,” he said, after a brief hail of profanity in which Mr. Lhota wondered aloud who, exactly, Mr. Bloomberg had been talking to.

“It’s wrong,” he told Mr. Glaser. “It’s just wrong.”

Mr. Lhota also spoke of the L line’s importance, as if his audience needed convincing.