The reductions in state aid, along with falling property tax revenues that are finally catching up with lower home values, are major sources of fiscal stress for many cities. Ben S. Bernanke, the Federal Reserve chairman, said in a speech this month that “many localities have been hard hit by reductions in state aid, which in 2008 accounted for about 30 percent of local revenues.” And Moody’s Investors Service, the ratings agency, said in a report last week that many states “are increasingly pushing down their problems to their local governments.” The Moody’s report warned that this would be “the toughest year for local governments since the economic downturn began.”

The cuts are a vivid illustration of a fact of fiscal life: budgetary pain flows downhill. Although state tax collections are finally improving again after the longest and deepest decline on record, they remain well below their prerecession levels. Stimulus money from Washington, which helped keep many states afloat over the last two years, is drying up. So states facing large deficits are proposing cuts in local aid. Ohio’s deficit is projected to be $8 billion over the course of its two-year budget — hence Governor Kasich’s proposed cuts.

Nebraska did not just reduce local aid, it eliminated it. Much less money was at stake — the law is estimated to save the state $22 million a year — but cities are nonetheless worried about the effects of the cuts. “This year, instead of cutting us all a certain percent, they went after the state aid totally, all 100 percent of it,” said Chris Beutler, the mayor of Lincoln. Mr. Beutler said that the cut would cost the city $1.8 million a year and force it to raise property taxes or cut services.

Direct aid represents only a fraction of the money flowing from states to local governments. When Mayor Michael R. Bloomberg of New York went to Albany last month, he said that by his count the budget Mr. Cuomo had proposed would reduce aid to the city by $2.1 billion, of which only around $300 million was in the form of direct municipal aid. The rest included a reduction of $1.4 billion to the city’s public schools, which in New York City are under the control of the mayor, and $380 million in cuts and cost shifts in social services. Mr. Bloomberg warned that the city would be forced to lay off more workers if the cuts went through.

Chris Hoene, the director of research for the National League of Cities, said that many states eliminated direct aid to cities — used to keep property taxes low, ease disparities among localities and help pay for general government services — after past recessions. Now, he said, most of the coming state cuts will be in the form of cuts to specific programs. Cuts to child health care, mental health programs, libraries or transportation will all have an impact on cities. On top of that, many states also have complex revenue-sharing programs with local governments, and a number of them are proposing to keep more of the money for themselves.

Mr. Hoene said the coming cuts were “a big, scary question mark” hanging over local governments. “Cities have made their estimates, and made cuts based on revenue projections,” he said. “The factor that they can’t control, and that’s concerning for them, is what’s going to happen in the deliberations in state legislatures over the next three months.”