With the City Council set to vote in Christine Quinn as its next speaker today, speculation is already growing about how the plum committee assignments and leadership posts will be doled out.

Political observers spent much of yesterday buzzing about who would lead the six open committees and which of Ms. Quinn’s council colleagues would get the leadership positions and their handsome salaries.

“Your guess is as good as mine,” Council Member Robert Jackson said when asked about speculation that he might be named chairman of the Education Committee.

A former union director and the lead plaintiff on a lawsuit claiming the city public schools were not all getting a fair amount of funding from the state, Mr. Jackson said he had not yet talked to Ms. Quinn about the job. He said, however, that he expects he is on the “short list.”

Ms. Quinn, meanwhile, was greeted by a mob of reporters and television cameras at her first public appearance since Monday, when she won the support she needed to put her candidacy over the top. She is expected win overwhelming support today to succeed Gifford Miller, who was just termed out of office.

In a dimly lit senior center on Bleeker Street, Ms. Quinn, 39, said she expects her relationship with the mayor to be “solid” and “professional.”

She said that while she has agreed with the mayor on some issues (the smoking ban) and disagreed with him on others (the West Side Stadium), he “is someone who clearly won the approval of the majority of New Yorkers.”

Mayor Bloomberg said he would be happy to work with Ms. Quinn if she was elected.

Ms. Quinn said her expected election as the first female and first openly gay speaker of the council would be an important break for those communities. “It sends a message that they can move to higher levels,” she said.

Her father, Lawrence Quinn, 79, a retired electrical worker who belonged to Local 444 of the International Union of Electrical Workers, which split from its original union due to its communist ties, joined her yesterday.

While Ms. Quinn’s phone was ringing madly as colleagues called to congratulate her, at least one council member from Brooklyn told The New York Sun he planned to abstain from today’s vote because he is upset about the process.

Council Member Charles Barron, who backed Ms. Quinn’s chief rival, Bill de Blasio, said members should not be outsourcing their votes to county leaders. “They were elected to make tough decisions independent of any union, of any business community, and of any county leader, especially,” he said.

Mr. Barron said that while he likes Ms. Quinn, it was a “disgrace” that Brooklyn did not muster enough votes to make one of its members speaker. He tacked some of the responsibility on Assemblyman Vito Lopez, the new party boss, for throwing his support behind Ms. Quinn, who is from Manhattan.

“It’s going to be war in Brooklyn,” Mr. Barron said. “I think Vito blew an opportunity to provide leadership just to get a few crumbs for a few people. I think that he made a big error.”

Mr. Lopez said his first preference would have been a speaker from Brooklyn, but that the math didn’t add up for Mr. de Blasio and he didn’t want the delegation cut out of the process.

The assemblyman said he has already met with five council members to find out what committee posts they want and was reaching out to all other members in the borough to do the same.

He said hopes to meet with Ms. Quinn later this week or early next to make “recommendations” and that he anticipated that Brooklyn members would fill four of the six vacant committee chairmanships.

Some are speculating that Council Member Erik Dilan, one of Mr. Lopez’s closest allies, will be named to head the housing committee. Mr. Lopez is chairman of the Assembly’s housing committee, so an ally in the council could be helpful.

Mr. Lopez said it was “premature” to speculate. Others said they expect Mr. de Blasio and possibly Council Member Lewis Fidler to get leadership positions.

An aide to Ms. Quinn said the committee assignments would not be voted on until later this month. The council also announced yesterday that the speaker’s chief of staff, Charles Meara, would remain in his job.