The City Council speaker, Christine Quinn, is proposing to extend city library service to six full days a week, expand preschool offerings, and help more families buy homes, part of what she called her growing effort to support middle-class residents in the city. She floated the proposals yesterday during her official response to Mayor Bloomberg’s preliminary budget.

Ms. Quinn said the proposals would go far to help New Yorkers.

The new council-backed initiatives would cost $45.4 million during the next fiscal year if they were agreed upon and enacted in the city budget.

Ms. Quinn also proposed a $300 renters’ tax credit for low- and middle-income tenants that would cost $261 million.

When asked about negotiating her budget with Mr. Bloomberg, Ms. Quinn said she doesn’t anticipate conflict.

“I expect that there will be productive, focused negotiations. There’s a lot of agreement in this budget,” she said. “The council and Bloomberg administration have been partners in the budget process in a way that councils and mayors have not been historically.”

Council officials said Ms. Quinn’s proposed budget adds $61 million to Mr. Bloomberg’s $57.1 billion preliminary budget. It calls for city agencies to reduce spending by $243 million and proposes that the Department of Education shift $17.9 million away from administrative and other programs and into classroom spending.

“One of the things that I was pleased to see in her budget was she did have some money-saving ideas,” Mr. Bloomberg, who is presenting his executive budget at the end of April, said.

Ms. Quinn’s budget response states that $12.3 million for classroom spending would come from the Panel for Education Policy, which replaced the Board of Education after Mr. Bloomberg won control of schools in 2002. Made up of 13 volunteers appointed by the mayor and borough presidents, it has been criticized for rubber-stamping Department of Education policy changes.

The panelists, who include Chancellor Joel Klein, are paid a stipend of $50 a meeting and do not earn a salary, yet there are 14 full-time employees, the council’s response states, citing the department’s latest Financial Status Report.

A spokesman for the mayor, Stu Loeser, said Ms. Quinn’s calculations are “incorrect.” Instead of $12.3 million, he said, the city spends $10,000 a year on the Panel for Education Policy for member stipends and audiovisual equipment. In addition, he said the 14 full-time support employees listed by the speaker “do not exist and they’re not being paid.”