States are increasingly alarmed that they could become collateral damage in Washington’s latest fiscal battle, fearing that the impasse could saddle them with across-the-board spending cuts that threaten to slow their fragile recoveries or thrust them back into recession.

Some states, like Maryland and Virginia, are vulnerable because their economies are heavily dependent on federal workers, federal contracts and military spending, which will face steep reductions if Congress allows the automatic cuts, known as sequestration, to begin next Friday. Others, including Illinois and South Dakota, are at risk because of their reliance on the types of federal grants that are scheduled to be cut. And many states simply fear that a heavy dose of federal austerity could weaken their economies, costing them jobs and much-needed tax revenue.

So as state officials begin to draw up their budgets for next year, some say that the biggest risk they see is not the weak housing market or the troubled European economy but the federal government. While the threat of big federal cuts to states has become something of a semiannual occurrence in recent years, state officials said in interviews that they fear that this time the federal government might not be crying wolf — and their hopes are dimming that a deal will be struck in Washington in time to avert the cuts.

The impact would be widespread as the cuts ripple across the nation over the next year.

Texas expects to see its education aid slashed hundreds of millions of dollars, which could force local school districts to fire teachers, if the cuts are not averted. Michigan officials say they are in no position to replace the lost federal dollars with state dollars, but worry about cuts to federal programs like the one that helps people heat their homes. Maryland is bracing not only for a blow to its economy, which depends on federal workers and contractors and the many private businesses that support them, but also for cuts in federal aid for schools, Head Start programs, a nutrition program for pregnant women, mothers and children, and job training programs, among others.