CONCORD, N.H. — Gov. Maggie Hassan said Monday she is optimistic that poor New Hampshire adults will begin receiving coverage by July under a proposal to use Medicaid funding to pay for private insurance.

A bipartisan Senate plan still must pass the Senate and House, but Hassan noted it received a positive recommendation last week from a Senate committee. She said she hopes lawmakers will act swiftly so an estimated 38,000 people can begin signing up for coverage under the state’s Medicaid managed care plan by May 1 and receive coverage starting July 1.

The plan calls for using federal money to buy the adults private coverage in 2016. The federal government would pick up the full cost of the plan until 2017. The expansion would end when federal funding drops below 100 percent unless the Legislature voted to continue it. The entire program also would end at the end of 2016 if the Legislature failed to reauthorize it.

The proposal hinges on New Hampshire winning federal approval to use Medicaid funding to buy private coverage. Under the proposal, the state would seek a federal waiver by March 31, 2015. If the federal government doesn’t approve a waiver by March 31, 2015, the expansion would end and the 38,000 adults would lose coverage.

Another 12,000 people would qualify under an existing program that subsidizes employer-based coverage. They would be covered in about 60 days after the plan became law. The Medicaid funding would pay for their coverage until 2017. Their coverage also would end if federal funding dropped below 100 percent.

The Senate plans to vote on the proposal on March 6. Supporters hope the House will be able to hold a hearing and vote on the bill by the end of March or early in April so the May 1 sign-up and July 1 coverage timeline can be made.

Hassan, who was in Washington for a meeting with the nation’s governors, said in a conference call with reporters that the timeline is possible.

“I think we’re working to do this as expeditiously as we can,” she said.

She said while in Washington she talked with the governors from Iowa and Arkansas, which are implementing similar plans to use federal money to buy health insurance.

“Both governors indicated a willingness to share details” about their programs, she said.