The expiration of federal stimulus funding for Medicaid has dealt a blow to states still struggling to recover from the economic downturn, according to figures released Thursday.

To compensate for the loss of extra federal Medicaid dollars this June, states have increased their spending on the program by an average of 29 percent in the current fiscal year.

Nearly every state also has turned to tough measures to trim Medicaid costs, such as eliminating benefits, reducing payment rates to doctors and hospitals, and increasing the co-payments they charge the poor and disabled served by the program.

Even so, more than half of state officials surveyed said there was a 50-50 chance their Medicaid programs — which are financed with a combination of state and federal funds — would face a budget shortfall as enrollment continues to rise.

Though widely anticipated, the findings reported in an annual survey of state officials by the nonpartisan Kaiser Family Foundation underscored the stress Medicaid has placed on state budgets.

The 2010 health-care overhaul law bars states from tightening their eligibility rules for Medicaid through 2014, when the program will be expanded to cover a larger share of the poor, almost entirely at the federal government’s expense.

All 29 Republican governors have written to President Obama and Congress pleading for relief from this “maintenance of effort” requirement.

“We’re on an unsustainable path,” said Mike Schrimpf, communications director for the Republican Governors Association. “Every year Medicaid takes up a greater share of most state budgets. . . . Every dollar spent on Medicaid necessarily comes out of somewhere else, so it’s taking away from every other item in the budget.”

Robin Rudowitz, a co-author of the Kaiser report, said the burden on states was largely the result of the timing of federal assistance.

The recession hit states with a double punch: Tax revenues nose-dived, while a surge in unemployed workers caused Medicaid rolls to swell.

The $103 billion in extra Medicaid funding that Congress sent to states through June of this year proved “enormously helpful,” Rudowitz said. For the first time in Medicaid’s history, states were able to cut back their Medicaid contributions — by an average of 11 percent in fiscal 2009 and 5 percent in fiscal 2010 — even as overall spending on the program rose to meet the increased need.

But when the last of the stimulus funding expired in June, Medi­caid enrollment remained above pre-recession levels and states were still a long way from full recovery. Today, “most states have higher unemployment rates than when the relief started,” Rudowitz said.

Tracy Gordon, a researcher at the Brookings Institution who specializes in state budgets, said there were signs of progress. The growth in Medicaid enrollment is slowing, and states have had six straight quarters of revenue growth.

Still, she said, state revenues remain at least 6 percent lower than pre-recession levels, and states are projecting a total of $46 billion in budget shortfalls for the fiscal year that will start next July.

That shortfall is “a lot less than at the height of the crisis,” said Gordon, “but the [extra] federal money is not available this time, and there’s a sense that the easy solutions are off the table — one-time things like selling off assets or borrowing from special funds.”

One option no one is pushing is another round of federal stimulus spending. “It really just boils down to the federal government’s budget challenges,” Gordon said. “In this environment, I think additional aid to the states is just not forthcoming.”

Vernon K. Smith, another author of the report, is worried that some of the cost-cutting measures states have employed since the recession could harm Medicaid recipients. “There is some concern that some of the provider cuts that have occurred year after year will eventually have an impact on access,” he said. “In states where rates were already low and are continuing to be cut, there is evidence that is already happening.For all the belt tightening, however, 22 states have expanded access to their Medicaid program this year. In addition, increasing numbers of states are trying approaches intended to save money while improving care, such as moving more of their Medicaid populations into managed-care plans or shifting patients needing long-term care from institutions to community settings.