Before school started this year, Nancy Morales, an Ecuadorian immigrant, spent several weeks walking up and down the streets of Jackson Heights with her 4-year-old daughter, Kelly, in tow. She was looking for a pre-kindergarten class that would accept her daughter without a Social Security number or proof of residence — the Morales family rents a room inside someone else’s apartment and doesn’t receive bills in the mail.

At churches and community centers, Ms. Morales knocked on doors and was turned away until the Latin American Integration Center helped her find a public school that would enroll her daughter in the publicly funded Universal Pre-Kindergarten program.

“I wanted her to go so she would start to learn and develop,” Ms. Morales, 29, said. “I want her to learn English.”

Ms. Morales was unable to work because she stayed home with her daughter, even though her family desperately needs the money. But even with Kelly in school during the week, Ms. Morales cannot hold down a job because the class is only for two hours a day. After it lets out, she spends the rest of the day with her daughter at the public library, reading children’s books, learning how to use computers (Ms. Morales is learning, too), and going over flash cards to help them both learn English.

This year, the City Council, under the leadership of Speaker Christine Quinn, announced a goal to make public, full-day pre-kindergarten classes available for all the city’s 4-year-olds. They had in mind parents like Ms. Morales, who need more than two hours of child care so they can work during the day, and who may not have the time or skills to prepare their children for school by themselves.

In September, the Department of Education made a step toward that goal by opening more than 2,000 full-day seats in addition to the more than 45,000 public pre-kindergarten slots in the city.

A court decision last week that ended the Campaign for Fiscal Equity lawsuit by setting $1.93 billion as the minimum amount New York City could receive in additional school aid could jeopardize efforts to expand the prekindergarten program, however.

“I’m very concerned that pre-K could be lost out in all of this,” the president of the United Federation of Teachers, Randi Weingarten, said. Ms. Weingarten is on the board of advisers for the Campaign for Fiscal Equity, the coalition of education advocates that brought the suit and had lobbied for at least $4.7 billion in aid for the city. “There are going to be some very important resource questions pitted against each other.”

The executive director of the Campaign for Fiscal Equity, Geri Palast, said the $1.93 billion, the lowest end of a range determined in a study commissioned by the state, did not factor in money for early childhood education.

“The 1.93 in 2004 dollars does not even consider pre-K,” she said.

When the Campaign for Fiscal Equity sued the state 13 years ago, saying New York City children weren’t receiving the sound, basic education required by the state constitution because of funding shortages, the focus was on improving high school education — the state had argued that its responsibility to provide a quality education only extended until eighth grade. The state’s highest court rejected that argument and ruled that a quality high school education was also a right.

Since then, education advocates have added pre-kindergarten to their list of priorities, saying research shows it is just as important as any other grade.

“Pre-K is fundamental if we’re going to succeed at a sound, basic education, if we’re going to have kids graduate from high school,” the president of the Schuyler Center for Analysis and Advocacy, an Albany-based public policy organization, Karen Schimke, said. “It’s a got-to-have. It’s not an option.”

In 1997, the state came close to making universal pre-kindergarten a reality when the speaker of the state Assembly, Sheldon Silver, introduced legislation for a statewide program that was projected to reach all 4-year-olds by 2002. Governor Pataki signed on in 1998, but the effort to reach all children by the 2002 deadline was hampered by a lack of funding.

The Campaign for Fiscal Equity lawsuit rekindled hope among early childhood advocates. As the lawsuit’s supporters lobbied for a change in the state funding formula that would allow state aid to be distributed more equitably, they also argued that pre-kindergarten be included in the formula for the first time. Currently, pre-kindergarten is funded by grants and is not included in the general education aid formula.

The court decision last week didn’t touch the formula, however, shifting the effort to fund pre-kindergarten into the political realm from the courts.

The Campaign for Fiscal Equity is now looking to Governor-elect Spitzer to ask for $4.7 billion — which includes money for pre-kindergarten — in his budget this February. Mr. Spitzer has said he will ask for more than $1.93 billion, though he has not specified how much more. In the past, he has indicated that he supports expanding prekindergarten.

Ms. Quinn said she is confident the new state administration will be supportive of the City Council’s efforts.

“Certainly we all would have liked more money than we got. That is what it is, that has to be a floor, not a ceiling,” she said. “We’re going to keep that fight going.”

Meanwhile, she says the City Council, in partnership with the mayor’s office and the Department of Education, is moving forward with its pre-kindergarten expansion efforts.

The first thing they must do is figure out how many programs already exist. Public pre-kindergarten programs are overseen by several agencies, including the Department of Education and the Administration of Children’s Services, that until now have communicated poorly. An interagency task force is currently mapping programs around the city to sort out who oversees them, how many children they serve, and where their money comes from.

The second step is finding out how many 4-year-olds are in the city, and how many parents like Ms. Morales are seeking full-day services.

“When we started, one of the first things I asked was, ‘Where are all the 4-year-olds?'” Ms. Quinn said. “When I asked that question, none of us had a good answer.”

The task force will conduct a census of 4-year-olds in the coming months by compiling information kept by city agencies and census data. By next year, the city should know how much money it needs from the state, if the state is willing to send it.