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Leaders in many states say they could dip into reserve funds or raise their own revenues to recover some of the lost funding, but many say their options are limited due to ongoing state-level financial troubles and local laws that could get in the way.

Timothy G. Kremer, executive director of the New York State School Boards Association, said his state will lose $164 million in education funding next school year if the federal cuts happen, and he added that school districts will have difficulty filling in even a portion of the costs because state law prevents local jurisdictions from raising school-funding property taxes without voter approval.

“The impact of the ‘fiscal cliff’ is made far more pronounced by the state’s property tax levy cap, which essentially limits the amount of revenue schools can raise locally,” Mr. Kremer said in a statement.

As congressional Republicans and the president work to reach a compromise on avoiding the cliff, national and local teachers’ union officials said they favor a plan that would raise taxes on only the top 2 percent of earners and make accompanying cuts that are lighter than Republicans want.

“It’s really high time that we made investments that strengthen our economy, and not ones that weaken it,” Ms. Gruber said. “Let’s ask CEOs and other rich Americans to pay their fair share.”