CONCORD, N.H. — House and Senate committees voted Thursday to recommend that New Hampshire expand Medicaid to an estimated 49,000 poor adults, but their plans differ on how to implement the expansion.

A key difference between the two bills is how quickly New Hampshire shifts the adults from a state-managed care program to private insurance through the federal insurance marketplace. The Republican-led Senate would shift people in 2015.

Gov. Maggie Hassan, a Democrat, and Democratic House leaders say that is not feasible because not enough insurance companies have expressed a willingness to offer products on the exchange.

The Senate panel voted 4-2 Thursday to give state officials a few more months to obtain a federal waiver needed to shift people onto private insurance. But Hassan’s spokesman said that still would not be enough time.

“The bill as amended still lacks workable, achievable and realistic timelines and includes no measures to ensure competition and cost-effectiveness on the exchange,” said Hassan spokesman Marc Goldberg.

Senate Republican Leader Jeb Bradley, of Wolfeboro, said Senate Republicans still want a firm deadline for the waiver to be approved or the coverage provided to the adults will end. “We are trying to accommodate some of the concerns that our timeline is too aggressive,” he said.

The House and Senate expansion plans are essentially the same for the first year, but take different approaches after that. Both start by using federal Medicaid funds to pay for private insurance for eligible adults already on employer-sponsored plans and enrolling others into a managed care program. The House plan continues that for two more years while the Senate proposal shifts people onto private insurance through the federal insurance marketplace.

Both plans would require federal waivers and would end the expansion if federal financial support fell below promised levels. The Senate would give the government one year to approve its use of the marketplace or the expansion would end.

The Senate plan also would end automatically at the end of three years when federal funding begins dropping below 100 percent unless the Legislature reauthorized it. The federal government plans to pick up 90 percent of the cost of Medicaid expansion in New Hampshire after the first three years.

Hassan and House Speaker Terie Norelli announced Wednesday they would compromise on another sticking point and agree to shift all the adults through the exchange.