Governor Terry McAuliffe (Evelyn Hockstein/For The Washington Post)

Gov. Terry McAuliffe announced a budget proposal Thursday that calls for expanding Medicaid in Virginia, sparking another sharp battle with a Republican-controlled legislature that has vowed to block his efforts for the third straight year.

This year McAuliffe is trying a new strategy that would expand the federal health-care program for the poor and disabled without state dollars and instead charge some hospitals a fee, known as a “provider assessment,” equal to 3 percent of their revenue. The cash is an untapped resource that McAuliffe said puts expansion within reach.

But in an effort to gain Republican support, his budget ties those projected Medicaid savings to some of their favorite initiatives. He argues that the state could afford everything from tax cuts to grants for small towns if they would only agree to extend coverage to 400,000 Virginians through the Affordable Care Act.

Republican leaders shrugged off the governor’s approach on Medicaid, but showed a willingness to consider McAuliffe’s proposed $1 billion investment in K-12 and higher education that could shape McAuliffe’s legacy at the midway point in his term.

“Two years from now, the budget I am announcing today will be winding down,” McAuliffe told a packed hearing during his annual budget speech. “Our nation’s fiscal and political environment may have devolved once again into chaos. We cannot control those outside forces, but we can accept responsibility for our own destiny. The question before us today is: How will we spend the coming two years?”

House Speaker William J. Howell (R-Stafford) said he doesn’t agree with McAuliffe’s rosy economic forecast and batted down any chance for a path to Medicaid expansion.

“I’m disappointed he kind of has overpromised, raised expectations,” he said. “I wish he had not included Medicaid expansion as part of his budget. He knows it isn’t going to pass.”

Indeed, Thursday’s speech brought into focus McAuliffe’s twin goals of Medicaid expansion and funding education, including a 2 percent pay raise for state workers. He wants to pay for an additional teacher in every Virginia public school, increase across-the-board spending to keep pace with enrollment growth and boost college financial aid. He also proposed a 2 percent pay raise for teachers.

House Majority Leader M. Kirkland Cox (R-Colonial Heights), who taught social studies for 30 years, said he’s wary of unintended consequences, such as whether counties and cities can afford their share of a teacher pay raise, Del. S. Chris Jones (R-Suffolk), chairman of the House Appropriations Committee, called the plan “very thoughtful” and said he anticipated “just nibbling around the edges” there.

“We’ve got a lot of common ground in the budget that we can agree on,” said Jones, who stood with McAuliffe as they took questions from reporters after the speech.

But it was the governor plan to use $156 million in projected Medicaid savings to pay for things Republicans like that rankled many in the party. For example, he would devote $3 million to the Jamestown-Yorktown Museum’s 2019 celebration in the back yard of Senate Majority Leader Thomas K. Norment (R-James City). Norment declined to comment.

He would pour $13 million into the Commonwealth Center for Advanced Manufacturing and $4 million into Go Virginia, a grant program championed by heavy hitters in business. Both are favorites of Cox’s.

Given McAuliffe’s call for new spending to spur economic development, Cox called it ironic that he would sacrifice thriving programs and ones with corporate buy-in.

“I don’t really care if I get targeted — but on the advanced manufacturing piece, I think he would agree that we’ve actually had some success there,” he said. “That part disturbs me.”

State GOP Chairman John Whitbeck called the approach “unconscionable” and said a third try for Medicaid is “shortsighted at best, and economic malpractice at worst.”

Even the governor’s Republican allies in the state legislature said the plan, as outlined, would have a hard time passing. “We’ve got people dying and living significantly shortened lives because of unaffordable access to quality health care,” said Sen. Emmett Hanger (R-Augusta), co-chairman of the Senate Finance Committee and one of the few Republicans who have voiced support for McAuliffe’s plan to expand the program. “It’s a tough sell politically.”

Michael Cassidy, chief executive of the left-leaning think tank Commonwealth Institute for Fiscal Analysis, rejected the notion that Medicaid expansion is dead on arrival because even states with conservative governors have accepted the dollars.

“Virginia lawmakers should not be obstinate in rejecting options when it’s clear other folks can get to yes,” he said.

It was unclear Thursday the lengths the debate over Medicaid might take this year, particularly after the governor has fought two battles over the issue. There was nearly a government shutdown over Medicaid in 2014. McAuliffe also called for Medicaid expansion in 2015 but never counted on the projected savings, making it easy for lawmakers to say no. Virginia is one of 21 states that have not expanded Medicaid.

The Virginia Hospital and Healthcare Association earlier this month reversed its opposition to a provider tax, giving McAuliffe a path to expansion. Traditionally the organization has resisted efforts to pay additional fees The association said the option could help hospitals that have complained of a financial crunch exacerbated by their mandate to provide free or reduced-price care to indigent patients.

“Now that the governor’s budget proposal is public, VHHA will evaluate it in light of the principles spelled out in the letter from earlier this month,” association President and CEO Sean T. Connaughton said in a statement. “While VHHA evaluates the budget proposal, it should be noted that Governor McAuliffe’s ongoing efforts to find compromise policy solutions to protect health care stability and access are appreciated.”

But even before McAuliffe unfurled his plan Thursday, Mark J. Rozell, dean of the School of Policy, Government and International Affairs at George Mason University in Arlington, said, he faced a hard sell: “Those minds are made up.”