Granted, the people who pack this library know from hardship. Many, including Ms. Negrimovskaya, come from the former Soviet Union. Many others are from China or Latin America. There is a smattering of Albanians, Poles and Pakistanis. Just a year ago, they were all reeling from the flooding, blackouts and stress wrought by Hurricane Sandy. To them, this boxy, plain library was a haven when it reopened three months after the storm to offer books, Internet access and even counseling.

Now if only the candidates who will win next week’s general election would take this place as seriously. Financing New York City’s three public library systems is an annual set piece of political theater, where City Hall proposes reduced budgets that are deplored and haggled over until the City Council restores much of the sum. According to a report last January by the Center for an Urban Future, since 2008 the Manhattan, Brooklyn and Queens libraries have endured cuts of nearly $65 million.

Library advocates said the current allocation of $106.7 million for all three systems is the first not to have cuts, though five years of decreased funds despite increased public demand has taken a toll — hours have been reduced, capital improvement has been postponed, and much-needed employees have not been hired.

“The libraries often can’t plan beyond a year because they don’t know what the budget is going to be,” said Julie Sandorf, president of the Charles H. Revson Foundation, which recently gave $10,000 grants to the Sheepshead Bay branch and four others. “It’s not like schools or parks, who start with a set budget. The libraries start from zero.”

Ms. Sandorf said that for $50 million more each year — “a rounding error in the city’s $70 billion budget” — all of the city’s libraries could be open 50 hours a week, instead of the current average of 43 hours. “If we are talking about a knowledge-based economy, this is what we need to do,” she said. “The problem is there is a huge gulf between the decision makers in this city who can pay for books or iPads and what is going on in every single library branch in the city.”

Shrinking budgets in Brooklyn resulted in the library system not having operating funds to hire any additional children’s librarians for five years until this year, said David Woloch, the Brooklyn system’s executive vice president for external affairs. And while the system’s 60 branches need $300 million in capital improvements, he said only $15 million was available this year, requiring triage to see whose roof or cooling system was in the worst shape.

Despite these challenges, branches like Sheepshead Bay offer countless services to an unending stream of people, including language and citizenship classes, arts and crafts, preschool story time, chess and even a Russian literature fan club.

Last Wednesday, a couple played Scrabble at a table while another couple studied for a nursing test. Nearby, a man browsed a selection of Korean movies, while another thumbed through recently arrived books in Russian. Upstairs, children did their homework or checked their e-mail.
“If you are going to be educated, you have to be in touch with the culture,” said Laura Sermassan, an immigrant from Romania who meets her three sons at the library each day after school. “It’s a point of integration into American culture. It’s a support.”

Ms. Negrimovskaya, in her office — where the shelf behind her desk has dictionaries in Yiddish, Russian, English and Chinese — was already looking forward to Tuesday’s gathering to mark Hurricane Sandy’s passing and the community’s rebound. She said people came alive when they were able to come back.
 
Then again, her neighbors have always been excited about the place. She recalled a woman who showed up in her slippers, eagerly asking how she could get on the Internet.

“I asked her if she had ever been on the Internet,” Ms. Negrimovskaya said. “She told me, ‘No, I never even saw a computer in Russia.’ I only asked her one more question: ‘Do you have a library card?’ ”
 
She smiled as she recalled the woman’s answer.
 
“Library card? I have a MetroCard!”