Virginia Gov. Terry McAuliffe waves a letter from the Center for Medicare and Medicaid Services during a news conference at the Patrick Henry Building in Richmond on Monday. (Bob Brown/AP)

Gov. Terry McAuliffe tried to shake up Virginia’s deadlocked Medicaid debate Monday by proposing a new budget that would expand the health-care program and shower a projected $225 million in related savings on teachers, state employees, pre-kindergarten programs and other Democratic priorities.

The governor’s proposal was a nonstarter in the Republican-dominated House, whose Appropriations Committee rejected the offer in favor of a spending plan that does not expand Medicaid under the federal health-care law known informally as Obamacare.

McAuliffe (D) unveiled his budget plan on the first day of a special legislative session, called after the Medicaid impasse prevented passage of a budget during the 60-day regular session that ended March 8.

Positions on expansion have only hardened in the past two weeks — a fact made especially clear Monday, as the House and Senate spent the opening day wrangling over an entirely symbolic issue: whose bill would be the starting point for budget negotiations, McAuliffe’s or one proposed by House Appropriations Committee Chairman S. Chris Jones (R-Suffolk).

That question remained unsettled by the time legislators adjourned. The House will return Tuesday night and expects to pass its budget by Wednesday. But the full Senate will not meet again until April 7, meaning negotiators will not have a Senate plan before them until then. Senate leaders said they needed additional time to consider McAuliffe’s plan.

The House and Senate did pass a “caboose bill” to make spending adjustments to the budget covering the current fiscal year, which concludes June 30.

State government could be forced to shut down if the legislature does not pass a budget by the start of the new fiscal year July 1. Any delay can make it hard for local governments, school districts and others that rely on state funding to set their own budgets.

Under the Affordable Care Act, states have the option to expand the health-care program for the poor and disabled to cover people making up to 138 percent of the poverty level. McAuliffe, Senate Democrats and three moderate Republicans in that evenly split chamber want to expand, saying it would help 400,000 needy Virginians and create 30,000 new jobs.House Republicans say the federal government is already too overextended to make good on its promise to pick up most of the $2 billion-a-year cost.

McAuliffe began the day by unveiling a two-year, $96 billion spending plan that calls for expanding traditional Medicaid. That represents a shift from the “private option” plan that the Senate had proposed — and McAuliffe had endorsed — during the regular session. Called Marketplace Virginia and intended to be more palatable to conservatives, the Senate plan would have used the Medicaid funds to buy private insurance for enrollees.

Some thought McAuliffe’s move back to traditional Medicaid was meant to correct for the Senate’s perceived strategic error — proffering its compromise marketplace plan too early in negotiations with the House.

“He set the reset button,” Del. Scott A. Surovell (D-Fairfax) said.

Republicans mocked the zigzagging from traditional Medicaid to Marketplace Virginia and back again, saying it represented the slapdash approach at the root of many of the health-care law’s problems. They renewed their calls to pass a “clean” budget and to consider Medicaid separately.

“We’ve gone from Medicaid expansion to Marketplace Virginia, and I think we’re back to Medicaid expansion,” said House Majority leader M. Kirkland Cox (R-Colonial Heights). “The message is: Clean budget now.”

McAuliffe said expanding Medicaid would save the state $225 million a year, primarily in funds it would otherwise pay hospitals for charity care. He proposed spending that money in the budget in a variety of ways, including giving a 2 percent raise to teachers and state employees.

McAuliffe said his expansion would be limited to a two-year “pilot program” that the state could extend if it is happy with it. He waved a letter that he said should allay Republican concerns about how quickly Virginia could pull back from expansion. Republicans have noted that federal officials have told Arkansas, which pioneered the private-option approach, that it must give enrollees seven months’ notice and provide everyone the opportunity to appeal cancellations.

Republicans said that the letter, from the federal Department of Health and Human Services’ Centers for Medicare and Medicaid Services, says nothing about how quickly a state can extricate itself from Medicaid expansion. It restates what the Supreme Court ruled in 2012: That Washington may not punish states, with fines or by withholding other Medicaid funds, that do not expand or discontinue expansion.

“I don’t know how you stand up a two-year program and just stop it,” said Del. John M. O’Bannon III (R-Henrico), who also questioned what would happen to the teacher raises and other spending premised on savings.

McAuliffe spokesman Brian Coy said the state would be allowed to end Medicaid expansion immediately at the end of the two years if it so desires because it would be set up as a limited program.

“The governor’s not proposing what they did in Arkansas,” Coy said. “We can walk away.”