Virginia Gov. Terry McAuliffe (D) released his final budget on Monday. (Salwan Georges/The Washington Post)

Gov. Terry McAuliffe (D) took one final swing at expanding Medicaid in the state budget he presented to lawmakers Monday, a two-year spending plan that also gives Republicans one of their most cherished goals: full funding of the state's rainy-day reserves.

McAuliffe based the budget of $115.9 billion on the premise that the state would accept federal money to expand Medicaid — something that Republicans have repeatedly resisted despite the fact that polls show strong support among Virginians.

The move would infuse more than $400 million into state coffers, allowing Virginia to balance its budget and fund other priorities, such as a raise for state employees and more money for education and mental health services.

“It’s long past time to take this fiscally responsible, common-sense step,” McAuliffe told lawmakers in his presentation.

McAuliffe’s plan represents about $1.7 billion in new spending.

This is the fourth straight year McAuliffe has tried to get the Republican-controlled legislature to go along with Medicaid expansion, but this time he believes he has a better shot at success.

Last month’s wave of Democratic wins in state elections erased the huge edge Republicans had in the 100-seat House of Delegates. Instead of a 66-to-34 advantage, Republicans are now faced with at least a 51-to-49 split, with three close races up for recounts that could lead to power-sharing or even a Democratic majority.

The state Senate stands at 21 to 19, with a Democratic lieutenant governor set to cast tiebreaking votes.

McAuliffe’s term runs out on Jan. 13, but he’ll be handing the reins to a fellow Democrat, Gov.-elect Ralph Northam, who has said he supports the same priorities. Northam said in an interview last week that he favors Medicaid expansion but will form a bipartisan group to overhaul the way the program is administered and seek cost savings.

Republican leaders cautioned Monday that they remain skeptical of McAuliffe’s plan for expansion but said they liked Northam’s openness to tying the issue to a Medicaid restructure.

“I’m very encouraged by the comments of the governor-elect,” said Del. S. Chris Jones­ (R-Suffolk), chairman of the House Appropriations Committee. “I think it’s realistic to expect there will be some additional coverage for Virginians.”

But Senate Majority Leader Thomas K. Norment Jr. (R-James City) said coverage may not come in the form that McAuliffe seeks.

“I would not be overly optimistic in seeing Medicaid expansion as the governor has repeatedly presented it,” Norment said. “I think we will look at some additional dollars in health-care coverage, just not with his . . . approach.”

The budget unveiled Monday makes plain the possible advantages of a Medicaid expansion: Some 300,000 uninsured Virginians would be expected to get coverage under the federal program, which provides coverage to those with low incomes. That’s the predicted uptake out of about 370,000 who are eligible.

Under the federal Affordable Care Act, federal money would cover 90 percent of the additional cost of expanding the program. McAuliffe proposed covering the remaining cost through a “provider assessment” on hospitals, an arrangement the state’s hospitals had agreed to in previous years.

The budget predicts savings of $421.7 million over the two-year period by taking the federal money — freeing up state resources to use on other priorities.

With state revenue collections running a bit higher than expected, McAuliffe proposed more than $1.7 billion in new spending. He included more than $500 million in public education spending and about $100 million to fund a pay raise of 2 percent for state ­employees.

But the shadow of the tax overhaul pending in Congress hangs over the spending document. Virginia budget officials said it’s impossible to predict all the ways a federal tax overhaul might affect state revenue, so they based the plan on current law. The General Assembly will have to reconcile the budget to federal changes once they come into focus early next year.

That uncertain climate is also part of McAuliffe’s justification for committing big dollars to the state’s reserve funds.

“We must build reserves to protect us against the risks associated with the federal government and national economic uncertainty,” McAuliffe said.

He proposed putting more than $270 million into the state’s cash reserve fund, which had dwindled during recent years of lean economic times. The shrinking of the state’s rainy-day reserves had set off alarms among bond rating agencies and threatened the state’s coveted AAA bond rating.

Restoring full funding has been a major goal of Republican lawmakers, who McAuliffe said might be more in the mood to compromise now that their grip on power is not so absolute.