A bipartisan group of governors came to Washington on Tuesday to urge President Obama and congressional leaders to act quickly to avert the “fiscal cliff,” warning that the series of budget cuts and tax increases set to take effect in January would rock their states.

The impact could be particularly dramatic locally, where Virginia and Maryland are grappling with the prospect of a broad cut in defense and other federal spending, key to both states’ economies.

In Virginia, the legislature has established a $30 million contingency fund to guard against federal reductions and the governor has asked agencies to prepare budgets that include across-the-board 4 percent cuts — just in case.

Fitch Ratings said Monday that the possibility that Congress will not avert the fiscal cliff poses the most significant credit risk to states in 2013.

Already, governors and mayors nationwide are saying that the uncertainty spawned by the deadlocked congressional negotiations is crimping economic activity and making budget planning an exercise in creativity.

“It is a very difficult time for all of us because we are trying to figure out what to do going forward,” said Gov. Gary R. Herbert (R-Utah). “It is almost like we have to prepare one budget if we solve it and one budget if they don’t solve it.”

In a late-morning White House meeting, members of the National Governors Association’s executive committee delivered that message to Obama and Vice President Biden. They also made a similar point in a meeting with congressional leaders on Capitol Hill later Tuesday, reminding lawmakers that their actions to solve the nation’s long-term budget problems will have immediate repercussions in state and local governments.

States rely on the federal government for about a third of their revenue, and the automatic spending cuts that are set to take effect in January would reduce funding for an array of social-service, education and housing programs. In addition, businesses that contract with the federal government also would face automatic budget cuts.

“States would be affected very differently, and for them, it adds to the uncertainty,” said Anne Stauffer, project director at the Pew Center on the States, which released a report last month on the state impacts.

In Charleston, S.C., longtime mayor Joseph R. Riley Jr. said he will present a budget to the city council on Wednesday that is based partly on conjecture.

“I am operating the city with nervous anticipation,” he said. “If we went over the fiscal cliff, I would have to quickly put into action major budget modifications.”

Going over the fiscal cliff would have the most direct impact on state budgets through the $110 billion in automatic spending cuts slated to begin in January if no agreement is reached to stop them.

Although some federal programs especially key for states — notably Medicaid — are exempt, many other federal grants to states would be cut. The Pew report said 18 percent of federal grant money would be subjected to the automatic hit. That includes Title I funding, which covers education programs for the poor and the disabled, medical research money, and health and human resource programs.

Those cuts would affect states before trickling down to local governments, making the reductions “perhaps the biggest threat to our metro economies,” according to the U.S. Conference of Mayors.

“What is insane is that this is a man-made disaster,” said Phoenix Mayor Greg Stanton (D), who said that Arizona would lose nearly 40,000 aerospace jobs and 12,000 government slots if Washington lawmakers do not agree on an alternative to the fiscal cliff.

With states already projecting an estimated $30.6 billion in shortfalls in their cumulative 2013 budgets, the added loss of federal money probably would result in major cuts in government services.

“There’s just no extra money sloshing around in the states, so I don’t expect that they’ll make up for federal cuts,” said Scott D. Pattison, executive director of the National Association of State Budget Officers.

But a far more serious hit could come to states as they absorb the effects of a sudden broad-based tax increase that would accompany the spending cuts. The Congressional Budget Office has predicted that the combination would push the national economy back into recession and cause the unemployment rate to rise above 9 percent by the end of next year.

That kind of economic deterioration probably would cause state tax receipts to drop, erasing gains that had finally begun after the economic crash. As a result, states would have less money flowing into their coffers just as federal assistance drops off.

“From that perspective, every state in the country is affected negatively,” said Virginia Secretary of Finance Ric Brown. “It’s the macro impact on demand for services, on income and sales taxes, which are the bread and butter for states.”

In Maryland, government forecasters predicted that the state would lose 100,000 jobs if lawmakers do not reach a resolution. But as officials prepare revenue projections for state budget makers, they say they have little choice but to hope for the best.

“Like most forecasters, we’ll be assuming that we don’t go over the fiscal cliff as it stands in current law, that somehow there will be a compromise that will mitigate the impact,” said Joseph Shapiro, a spokesman for the Maryland comptroller’s office.

Any deal probably would involve a dramatic reduction in federal spending that could affect state budgets. Some expiring tax provisions also could be allowed to remain in place.

“I don’t even know that it matters what the construct of the deal is — I think we all realize that federal spending will decline, one way or the other,” added Betsey Daley, staff director of the Virginia Senate Finance Committee and chairman of the National Association of Legislative Fiscal Offices. “We just want to know when and how much, and no one can tell you that. That is the biggest challenge — dealing in this vacuum of knowledge.”