The fictions behind the mayor’s accounting include crediting the unions with savings achieved by purging insurance rolls of people who were ineligible for benefits — thereby reclaiming money that belonged to taxpayers, not to the workforce.

They also include inflating projected hikes in health insurance premiums, pressuring the city’s carriers and their state regulator to hold down increases and crediting the unions with the difference between the initial outsized projection and the final bill.

In recent days, Mr. de Blasio has sounded downcast, according to aides who have spoken with him. The manager of his mayoral campaign has returned to help. And his team is considering focus groups and a poll to refine the mayor’s message to New Yorkers who may have soured on him.

How Mr. de Blasio reached this point is a story of accumulated slights, political miscalculations and the slowness of members of his inner circle, almost none of whom have close ties to law enforcement, in reacting to the warning signs of what would become the gravest crisis of his young mayoralty.

Mr. de Blasio has made few public appearances since Officer Ramos and his partner, Officer Wenjian Liu, were fatally shot in Brooklyn on Dec. 20.

The mayor has avoided unscripted interactions with the news media, taking no questions from reporters since Monday afternoon. On Friday, his aides would not disclose his location until after 9 p.m., moments before he arrived for the final minutes of a wake and memorial service for Officer Ramos.

People close to de Blasio also said he supported the Garner protesters not because he backed their position, but because he wanted to avoid antagonizing them in the wake of the grand jury decision not to indict the officer who killed Garner.

Notoriously late Mayor Bill de Blasio kept more than 100 people waiting at the gate to board a JetBlue flight from JFK Airport to Puerto Rico last month because he was running late and had the plane held for him, DNAinfo New York has learned.

It is unclear why the mayor was late for the plane, but his NYPD security personnel had to radio the airline security to hold it for him, sources said.