Virginia Gov. Terry McAuliffe gestures during a news conference at the Patrick Henry Building in Richmond on March 24. (Bob Brown/AP)

Virginia legislators return to the Capitol on Wednesday intending to wrap up some unfinished business but with no plans to tackle the budget and Medicaid stalemates that could ultimately shut down the state government.

The General Assembly will hold its annual “veto session” to complete work from the regular session that ended March 8. But no action is expected on the biggest issues looming over Richmond: Medicaid expansion and, because that matter was folded into the Senate’s two-year, $96 billion state spending plan, the budget.

Unless the chambers decide to suspend their rules and take up matters not on their agendas, they will finish the day as they started — with no plan to fund schools, colleges, local governments and all manner of state services for the next two years.

There will not even be rival budgets for negotiators to discuss. Because the House and the Senate have been unwilling to vote on the other’s budget, they do not have competing plans in conference, where teams from both chambers could begin hashing out differences.

Legislators on both sides of the aisle expressed hope that the deadlock will be broken by July 1, the start of the next fiscal year. But they’re not expecting to see any action Wednesday beyond the now-predictable floor speeches by legislators for or against expanding Medicaid under the federal Affordable Care Act.

Gov. Terry McAuliffe (D) and a narrow majority in the evenly divided Senate say expanding Medicaid would help 400,000 uninsured Virginians and help the state’s economy. The GOP-dominated House says that Washington cannot afford to keep its promise to pay most of the cost, estimated at $2 billion a year.

“I don’t expect that there’s going to be any substantial movement until the latter part of May, early part of June,” said House Minority Leader David J. Toscano (D-Charlottesville).

Toscano and several other legislators expressed confidence that core functions of state government would continue to operate even if July 1 comes and goes without passage of a budget. That would be uncharted territory for Virginia, where the General Assembly has never failed to pass a budget by that deadline. It has come close several times, most narrowly in 2006, when the House dug in against the funds that then-governor Timothy M. Kaine (D) wanted for transportation.

Back then, Kaine’s administration maintained that the governor had the authority to continue funding critical state services. Then-attorney general Robert F. McDonnell (R) disagreed. “The Constitution states that no funds are to be paid out of the state treasury unless appropriated by law by the General Assembly,” McDonnell wrote in an advisory opinion.

McDonnell conceded that the governor had the power to spend state money under certain emergency conditions, but he said it was questionable if the legislature’s failure to act amounted to a qualifying emergency. He also concluded that the Virginia Constitution did not expressly grant the governor the power to make emergency expenditures when, in the absence of a budget, “there are no existing appropriations made by law.”

“I can’t imagine we’re going to toss the prisoners a bag of sandwiches and say, ‘Take care of yourselves,’” said Sen. Dave W. Marsden (D-Fairfax). “Here in late April, we have plenty of time to wrap this up before we get into the death-star scenario.”

The offices of McAuliffe and Attorney General Mark R. Herring (D) declined to comment on whether they have been exploring whether the governor has the authority to keep state government at least partially open without a budget.

But legislators said they are surely looking into it, even has they hold out hope that it never comes to pass.

“I imagine that those discussions are going on within the executive branch, because they have a responsibility to make sure that public safety and core services are maintained in the event there is no budget,” Toscano said.

A.E. Dick Howard, a constitutional law expert at the University of Virginia, said there would have to be a way to keep essential functions of government operating. He noted that the constitution vests the chief executive with certain powers that “at least raise the question of whether the governor has some inherent power to save the commonwealth from destruction.”

“The constitution is not a suicide pact,” Howard said. “No matter what the language of the constitution, it simply does not make sense to read it as saying the governor’s hands are tied, rendering him helpless based on a clear danger to the public safety, health and welfare.”

Howard likened the governor keeping core government services operating to a court issuing a temporary injunction to preserve the status quo until the merits of a case are decided.

“I think you could argue the governor has a comparable power to keep things as they are, [to] keep them going until you get a policy decision,” Howard said.

During Wednesday’s session, legislators will approve or reject amendments that McAuliffe made to about 60 bills passed during the regular session and consider overriding McAuliffe’s veto of five bills.

Of the five, legislators said, the most likely to be overridden is McAuliffe’s veto of a bill brought by Sen. Richard H. Black (R-Loudoun). It would prevent the state government from censoring the content of sermons made by Virginia National Guard chaplains.

In vetoing the measure, McAuliffe said he did not want National Guard members to be “subjected to sectarian proselytizing” at events where attendance is mandatory.