Talk in City Council chambers about the rosy budget Mayor Bloomberg proposed last month has grown more hostile in recent days.

Mr. Bloomberg agreed months ago to add $1.3 billion for school construction projects, and then, in the revised budget he released last month, he added $125 million to his original proposal, to ease cuts and to finance new programs. Even the council speaker, Gifford Miller, initially said he was glad the mayor adopted some of the council’s requests. In contrast to past years, nonprofit institutions and lobbyists trying to secure more money for their causes have not been as vocal in their criticism of the budget, which seems this year to be more of a solo effort by the council’s Democratic majority.

Lately, however, the speaker’s rhetoric has become harsher, and Mr. Miller, one of four Democrats campaigning to challenge Mr. Bloomberg, announced this week the launch of a Web site that breaks down budget cuts by neighborhood.

A spokesman for the mayor, Jordan Barowitz, said yesterday that the administration looked forward to negotiating with the council once Mr. Miller was “done with his PR stunts.”

Mr. Miller denied that creating the Web site was a political move.

“I’m the speaker of the New York City Council and I’m only going to adopt a budget that protects neighborhoods,” he told reporters during a news conference. “That’s not political. That’s my job.”

He and others in the council have said that while the proposed budget, which calls for spending $49.7 billion in the fiscal year that starts July 1, is easier to swallow than past Bloomberg budgets, it would drastically decrease city funds for libraries, college scholarships, child health clinics, and more. The Democrats have criticized the mayor for eliminating funds they added last year rather than including them in the permanent “baseline.”

Council Member Domenic Recchia Jr., a Democrat from Brooklyn and a Miller supporter, took aim at the administration during a hearing last week.

Mr. Recchia, chairman of the council’s cultural affairs committee, demanded that library officials, who said they would have to cut one day of service at every library under the existing budget, stand up to the mayor.

“The mayor has a lot more money than the City Council does,” Mr. Recchia told the library officials. “How come he is not giving that money to the libraries? He’s supposed to be the education mayor!”

The president of the New York Public Library, Paul LeClerc, a former college president who with his round spectacles looked especially professorial next to the brash Mr. Recchia, told the council member the library badly needs more money.

Mr. Recchia made the point that the council fights for libraries every year and restores funds, but that the administration never steps up.

This hearing did not draw much public attention, partly because many believe that the existing holes will be patched up before the final budget is passed. It’s the regular budget dance, some analysts said.

Still, some students of the budget process said that while mayoral candidates’ actions surely are political, it is shrewd for Mr. Miller to drum up attention over disagreements in the budget.

A spokesman for Mr. Miller, Stephen Sigmund, said the council has been consistent from year to year in its approach to the budget, and he said the advocates of more generous spending have not gone away. They’ll be camped out at City Hall once negotiations start later this month, he said.

Yet reaction to this year’s budget has been tempered.

“The day the budget was released, there were noticeably fewer lobbyists and advocates around City Hall,” a spokesman for the city’s Independent Budget Office, Douglas Turetsky, said. “They seemingly knew the mayor was partially or fully restoring many of the previously proposed cuts.”

One point of contention, Mr. Turetsky said, could be new spending proposals the council has yet to unveil.

“It’s a smart political move,” the executive director of Citizens Union, Dick Dadey, said. “I think it’s smart for the speaker to try to take down to a neighborhood level the impact of the cuts that are still on the table. It’s shrewd given the fact that he doesn’t have that much room to play with.”

And he doesn’t have much time. The current budget process is Mr. Miller’s last opportunity to define himself as speaker before he becomes a lame duck – because of term limits, he cannot seek re-election to the council – and perhaps his best opportunity to differentiate himself from his three rivals in the Democratic campaign.

“It’s also an opportunity to deliver in a way that some of the other candidates are not in a position to,” Mr. Dadey said. “He does have the power of the purse strings here that his other Democratic opponents do not.”

An irony of the 2005 campaign is that Mr. Miller, who hopes to run against Mr. Bloomberg this fall, will first have to come to an agreement with the mayor on a balanced budget by summer.