“People are calling 311 and coming up to me and saying, ‘Where’s my check?’ ” said Councilman Simcha Felder, who represents Brooklyn. “Now the mayor is saying, ‘Guess what? The check is not in the mail, and we’re going to increase your taxes.’ It’s like saying: ‘We want to cut off your fingers. If you don’t let us do that, next year things are going to be so terrible we’re going to cut off your legs.’ ”

Even Council Speaker Christine C. Quinn, who has worked closely with Mr. Bloomberg on numerous issues, did not mince words, raising concerns about the canceled rebates, as well as the effect that the proposed cuts would have on education, public safety and public housing.

“Specifically, we are troubled by the proposed withdrawal of the $400 homeowner tax rebate that has been scheduled for later this year,” she said in a statement. “Many families will be counting on that money in their annual budget, and to withdraw it could cause a big hole in their pockets.”

Image A firefighter officers' promotion ceremony on Wednesday. The mayor wants to reduce training for probationary firefighters to 18 weeks, from 23 weeks. Credit... Uli Seit for The New York Times

In making his case, the mayor presented slide after slide of bar charts to demonstrate the impact of the global economic crisis on the city.

And he recited a grim litany of statistics: $500 billion in losses on Wall Street, a loss of 147,000 jobs in the financial sector, a projected $2.6 billion drop in city revenues. And, he said, the city would need to make up for an $8.4 billion shortfall in the pension system through fiscal year 2016 if the system, now down 20 percent in market value, posts a similar loss at the end of the current fiscal year. Mr. Bloomberg said it gave him no pleasure to add another deflating number to the mix: a loss of 3,000 jobs from the municipal work force, including 500 layoffs. And he warned that it was impossible to predict whether more cuts would be needed.

“If things get worse and we have to cut back more, I don’t think anybody can say, for sure, ‘You are protected,’ ” he said.