While the GOP-dominated Virginia House is expected to shoot down the proposed $2 billion-a-year expansion to Medicaid, Gov. Terry McAuliffe says he’s holding out hope that expansion will come at some point — if not during the session. (Bob Brown/AP)

— Republican leaders of Virginia’s House of Delegates, who have staunchly opposed Medicaid expansion all year, plan to put the question to a floor vote as early as Thursday in a special legislative session.

The GOP-dominated chamber is widely expected to shoot down the proposed $2 billion-a-year expansion, although a few conservative legislators have expressed fears that the measure might defy expectations and pass — just as a then-record tax hike did when Democrat Mark R. Warner was governor a decade ago.

Legislators return to Richmond three months after the GOP broke a bitter stalemate over Medicaid in a way that inflamed partisan rancor and drew the attention of the FBI, which has been investigating whether Republicans used a job offer to entice a Democrat to suddenly quit the evenly tied Senate.

The partisan rhetoric has cooled a bit since then. Ten days ago, Gov. Terry McAuliffe (D) pulled back from a threat to defy the legislature and find a way to insure 400,000 Virginians unilaterally. And on Monday, McAuliffe and House Speaker William J. Howell (R-Stafford) stood side by side to announce a bipartisan plan to close a $2.4 billion budget shortfall — a matter that will also come up for a vote during what is expected to be a two-day session.

There has been no indication that House Republicans have warmed to Medicaid expansion, even under the latest iteration, which proposes using some of the federal money to help low-income Virginians buy private insurance through their employers.

Howell said he called the special session to honor a promise to give the issue a full and fair hearing. Asked at his news conference with McAuliffe this week whether there were any Medicaid expansion bills that he favored, Howell said: “Haven’t seen any.”

McAuliffe, calling himself the “ultimate optimist,” held out hope for expansion at some point — if not during the session.

“I do believe if we sit in a room . . . for a couple hours, we can hash this thing out and do what’s in the best interests of the commonwealth of Virginia,” he said.

There are a few bills in the mix, but the one expected to come to the floor is sponsored by Del. Thomas Davis Rust (R-Fairfax), the lone House Republican to favor earlier plans for expanding Medicaid under the Affordable Care Act.

Under the federal health-care law, states may extend Medicaid to people with incomes up to 133 percent of the federal poverty line, which is $23,850 a year for a family of four. The federal government has pledged to pay most of the cost, about $2 billion a year in Virginia. McAuliffe, Democrats and three moderate Republicans in the Senate have favored expansion, saying it will return federal tax dollars to the state, help needy residents and create jobs. The House has questioned Washington’s ability to foot the bill and has objected to creating a new entitlement; currently, the state’s Medicaid program does not cover able-bodied adults.

Rust’s plan would use federal Medicaid funds to help people pay for private insurance that they already have the option to purchase through their employers but cannot afford. His plan also would expand health coverage through waivers and a complex series of rule changes.

“When we get into the final product, hopefully it’s almost like a block grant,” Rust said.

If, as many Republicans fear, the federal government begins to shift the cost burden to states, Rust said, his programs would disappear. However, according to an analysis from the state Department of Medical Assistance Services, the programs set up by his bill would save the state $150 million per year, he said.

Even Rust conceded that his plan will not be an easy sell in the House.

“Obviously it’s going to be a steep hill to climb,” he said.

But there are at least a few Republican legislators who fear that the House will approve Rust’s plan. They recall what happened in 2004, when then-governor Warner’s $1.6 billion tax package made it to the House floor — and passed.

“You recall in 2004, everybody was against Mark Warner’s tax increase and it was brought to the floor, and the general understanding was that it wouldn’t pass, and look what happened,” said Del. Mark J. Berg (R-Frederick).

Suspicions among some conservatives were heightened during passage of the budget in June, with the last-minute discovery of language that McAuliffe might have been able to use to argue that money for expansion had already been appropriated. Despite assurances from GOP leaders that the funding was there if, and only if, a Medicaid commission signed off on expansion, conservative legislators insisted that the language be removed.

“People are kind of gun shy after that fight that we had last time, when assurances were given that there was nothing there, but lo and behold there was,” said Del. Robert G. Marshall (R-Prince William).

Another sign of Republican anxiety popped up this week, as Del. Mark L. Cole (R-Spotsylvania) filed a bill authorizing the speaker to hire a lawyer to represent the House to “halt any attempt by the Governor to expand the Medicaid program without the explicit approval of the General Assembly.”

Yet some other conservatives said they were confident that they had successfully blocked any chance for unilateral action back in June, with a budget amendment that removed the language that some opposed.

Sen. Thomas A. Garrett Jr. (R-Louisa), who pushed hard for that amendment, said he had little fear that the special session will pave the way for expansion.

“I’ve got no problem with the daggone thing getting to the floor,” he said. “I’d be the first one to hoist a red flag if I think there’s some sort of subterfuge, but I don’t see it.”

Jenna Portnoy contributed to this report.