The mayor of New York, Michael Bloomberg, presented two budgets on Monday which many described as the "worse-case scenario" and an "even worse-case scenario".
Mr Bloomberg faces a potential budget shortfall of $6bn (£3.75bn).
His first proposal involves cuts of $600m resulting in 4,500 redundancies, and he described it as "painful".
The second, for cuts of $1bn, was "devastating" but would have to be enforced if assistance from New York state was not forthcoming.
Having already introduced a huge rise in property taxes and subway fares, the Republican mayor has now been tagged by the press "Mike the Knife" and "Gloomberg".
He admitted being "a little sad and a little angry" about the proposals, but added: "If you're afraid of these facts, I can't help you."
The lower cut would inflict the biggest number of redundancies in the past 10 years and be felt throughout the city.
A dozen children's clinics, and zoos in Brooklyn and Queens would be closed, renovation of the lion house and baboon house at the Bronx zoo halted, the lights on the east river bridges turned off, and rush-hour services by the Staten Island ferry reduced.
The bigger one would cost 10,000 jobs and close 40 fire stations, all the city swimming pools, and all after-school programmes.
Much of the deficit is the direct and indirect result of the terrorist attacks on September 11. With stock prices plunging, tourism fading, extra security costs and the national economy weak, the city's coffers are empty.
Given that it is also struggling with a huge deficit, New York state is unlikely to give the mayor all the help he wants.
Mr Bloomberg's popularity plunged to 31% late last year, almost a historic low for any city mayor, after he pushed through an 18% property tax increase. A New York Times poll in January showed that 53% of New Yorkers disapproved of his handling of the job.
Now he is is embroiled in a bitter dispute with the public service unions, which are resisting his proposals.
He denied that presenting two budgets was a scare tactic. "It is an insurance policy," he said. "You don't think you're going to die when you buy an insurance policy, but it's kind of imprudent not to have one."