Topeka ? Kansas legislators struggled Tuesday to get a handle on rising costs for Medicaid and other social services as a state Senate committee resumed work on the next state budget.

The Senate Ways and Means Committee reviewed projections that existing services will cost the state an additional $44 million during the fiscal year that begins July 1. Most of the new dollars would be needed for Medicaid, which covers health care for the poor, needy and disabled.

The projections also assume that Republican Gov. Sam Brownback’s efforts to overhaul the $2.9 billion-a-year Medicaid program will result in some savings. The state officials and legislative researchers who prepared the new numbers said the administration believes costs would rise by an additional $13 million without the overhaul.

The overhaul will turn management of the entire program over to three private companies, starting in January. But Senate committee members from both parties were skeptical that the change will create savings, because Brownback has promised that the state won’t sacrifice coverage for Medicaid participants or cut payments to health care providers.

“Common sense and logic tells me that it’s unlikely,” said Sen. John Vratil, a Leawood Republican. “I don’t know how those numbers compute.”

The committee’s proposed budget is likely to be about $14.1 billion for the next fiscal year. Legislators were close to taking final action last month on a compromise plan that covered most of the spending, but the agreement between House and Senate negotiators unraveled just before lawmakers adjourned for their annual spring break. The full Legislature reconvenes April 25.

New revenue projections released last week, reflecting a growing economy, gave lawmakers an additional $252 million cushion. But Brownback is pushing for income tax cuts to stimulate economic growth, and some lawmakers want some additional funds to go to public schools.

The new cost figures for social services replace projections made in November and reflect a growing number of people participating in Medicaid and other services. As of last month, the state was providing medical coverage for almost 387,000 people, up nearly 6 percent from March 2011.

Brownback spokeswoman Sherriene Jones-Sontag said those numbers demonstrate the need to overhaul Medicaid. Renamed KanCare, it would be a managed-care program, with each contractor operating statewide to give participants a choice of coverage. Most Medicaid participants already have managed-care coverage, but the overhaul is the first time Kansas has tried that approach with disabled and elderly residents needing expensive, long-term services.

Brownback contends the state will save money by better coordinating services and improving participants’ overall health. The administration projects the state’s savings at $368 million over the next five years.

“Without reforms in Medicaid so that we can find these savings, it will start impacting other parts of the budget,” Jones-Sontag said.

But Sen. Laura Kelly, of Topeka, the ranking Democrat on the Ways and Means Committee, said she doesn’t expect savings immediately.

“We’re not yet there,” she said. “We have yet to be able to make the math work.”