Advocates protest the city's proposed cuts to after-school programs during a rally outside City Hall today.

The city would spend $387 million more on its schools next year and hire more teachers under the budget proposal Mayor Bloomberg unveiled today.

But it would also slash spending to after-school programs, leaving 27,000 children who currently attend city-funded programs without care.

“I’m concerned,” Bloomberg said about the after-school cuts during a press conference about the budget today at City Hall. He said the programs are “extremely valuable” for working families but had unfortunately fallen victim to scarce resources. “We cannot do everything for everybody,” he said.

Advocates from Upper Manhattan gathered on the steps of City Hall in protest right after Bloomberg’s presentation, and critics of the mayor’s budget said the child-care cuts would prove short-sighted.

“These are dollars that allow parents to go to work and pay taxes; cutting them will only force more families to seek public assistance and add to taxpayer costs,” said Manhattan Borough President and mayoral candidate Scott Stringer in a statement.

But both the mayor and City Council Speaker Christine Quinn signaled that the toll could be lessened by the time a final budget is set by July 1.

At a press conference shortly after Bloomberg’s presentation, Quinn said reversing the child-care cuts would be her top priority during the next two months of budget negotiations. Last year, the budget negotiation process ended with some restorations for child care and, at the last moment, averted thousands of teacher layoffs that Bloomberg had threatened.

“If there is an openness to negotiations then I’m very optimistic,” Quinn said about the opportunity to shift more funds to after-school programs. Reversing the cuts would be a political win for each City Council member and especially for Quinn, who is seen as Bloomberg’s choice to succeed him.

Robert Jackson, the council’s education committee chair, vowed to turn back the cuts, which would eliminate thousands of child-care slots in his Northern Manhattan district. “If we have to dance to come to the end and reach an agreement, we will dance,” he said.

Quinn and other members of the council took credit for one change that happened between Bloomberg’s preliminary budget proposal and now. As Chancellor Dennis Walcott had promised and City Council sources indicated on Wednesday, the city is not calling for any reduction in the size of the Department of Education’s teaching corps. Instead, Bloomberg said today, it would actually add teaching positions for the first time after years of budget cuts.

Last year, the city lost 1,800 teaching jobs to attrition. Bloomberg said today the city would replace all teachers who leave and also likely add positions, for a total of 2,500 new hires.

The mayor’s preliminary budget, released in February, had also called for a $30 million cut in funds for overtime payments to Department of Education employees. That cut was eliminated, and a Department of Education spokesman, Matthew Mittenthal, said principals could opt to pay for after-school programs of their own using the “per session” funds.

United Federation of Teachers President Michael Mulgrew gave the budget a positive review but did not address the after-school cuts. “New York City has lost thousands of teachers over the last few years and it’s good news to hear that we will be adding educators to the system,” he said. “I can’t thank the City Council enough for making education a priority.”

But Mulgrew chided Bloomberg for saying during his press conference that he hoped the union would engage in “serious discussions” around new teacher evaluations, noting that the city, not the union, had walked out of talks in December.

“There’s no substantive reason why a final agreement should not be reached very quickly,” Bloomberg had said. “The longer the UFT waits, however, the longer it will take our schools to get the money they need and that they deserve.”

That’s because Gov. Andrew Cuomo has pledged to attach next year’s increases in school aid to teacher evaluation agreements: Districts that don’t finalize new evaluations by January 2013 won’t see their state aid grow. Not meeting the deadline could force the city to forgo $300 million for the year — nearly the same amount by which the DOE’s budget is slated to grow — and make deep midyear cuts to the Department of Education.