But all of the news will not be bleak. The Bloomberg administration said that it would open 10 new senior centers, each serving 250 to 300 people. One of the centers will cater to the visually impaired, while another will be designed to serve gay, lesbian, bisexual and transgender older people.

Heeding calls from members of the Council and advocates for children from low-income families, the mayor retreated from his initial budget proposal to eliminate almost 16,000 child care slots.

The city said it would preserve 4,400 of the 16,000 slots for low-income children at day care centers that faced elimination. An additional 10,500 slots will be covered by the Department of Youth and Community Development’s Out-of-School Time program, which provides after-school recreational and academic programs. The total cost is about $40 million.

That leaves more than 1,000 slots facing elimination, though the Council may provide additional money as it finishes up the budget over the coming weeks.

“While it is a step in the right direction, it is unclear if what the administration has put on the table is really an appropriate solution to the significant reduction of funding to the child care system,” said Council Member Annabel Palma, chairwoman of the General Welfare Committee. “More conversations and details are needed since it is unclear how services can remain intact for all 16,500 children with $40 million instead of $91 million; it is also unclear what the impact will be on existing out-of-school programs, providers, child care centers and classrooms.”

The city has benefited from better-than-expected tax revenue, with money from banking taxes up as Wall Street has rebounded. Personal income taxes are also strong, about 9 percent higher so far this fiscal year compared with the previous year, according to the Independent Budget Office. In addition, sales tax revenue is up slightly.

Council members seemed universally upset by the budget — both the content and presentation.

Several dismissed the $40 million that the administration had touted in additional child care funding as a “shell game” because the net result was still a $50 million drop in funding compared to last year. They also said the administration was unwilling to consider any tax increases, such as a tax on the wealthy, and unwilling to tap more money out of a health care retirement fund.