But defiance of the mandate is running high among some workers. In a protest outside the mayor’s residence, Gracie Mansion, on Thursday, many demonstrators wore sweatshirts and shirts bearing Fire Department engine and ladder company numbers from across the city. Union leaders led chants of “Hold the line!” and took aim at Mr. de Blasio for ordering vaccinations on what they said was too short a timeline.

Andrew Ansbro, the president of the Uniformed Firefighters Association, a firefighters’ union, said he had instructed all his members — vaccinated or not — to come to work on Monday in hopes of demonstrating that if any are turned away, the possible loss of life of life caused by understaffing would be on the mayor’s head.

“It’s his choice to put the lives he’s entrusted with in jeopardy,” Mr. Ansbro told the protesters.

With the mayoral election looming next Tuesday, Curtis Sliwa, the Republican contender and an opponent of the vaccine mandate, also attended Thursday’s protest and said that there would soon be “garbage everywhere” if sanitation workers stay home.

“The city is in bad shape now, and it’ll be in worse shape when you call 911,” Mr. Sliwa said.

The Democratic mayoral nominee and overwhelming favorite, Eric Adams, the Brooklyn borough president, supports the mandate, but he has said he would have worked more closely with unions than Mr. de Blasio did to implement it.

The mandate applies to roughly 160,000 city employees at some three dozen agencies, including some with very high vaccination rates among their staff, such as the Landmarks Preservation Commission, with a perfect 100 percent, and the Mayor’s Office at 96 percent. An additional 140,000 city workers, mainly hospital, public health and school employees, were already required to be vaccinated under earlier mandates.