Democratic Gov. Terry McAuliffe’s key priority this year, expanding Medicaid in Virginia under the Affordable Care Act, got a boost Wednesday with a new estimate showing that the program would save far more money than previously thought.

The expansion, along with other savings expected under the federal health-care law, is now expected to save Virginia more than $1 billion through 2022, according to William A. Hazel Jr., Virginia’s secretary of health and human resources. Previously, the new programs were projected to cost the state $137 million over that period.

The dramatic swing may not help McAuliffe push the measure through a Republican-controlled House of Delegates, where leaders have said they will steadfastly oppose Medicaid expansion. Republicans say that the program improperly expands the role of government — and that the federal government can’t afford it.

“I have not had a chance to look at these numbers. But my position has not changed,” said the House Appropriations Committee chairman, S. Chris Jones (R-Suffolk). “Reforms have to come first. And they have to be real.”

Hazel went over the numbers Wednesday in a brief meeting with the General Assembly’s finance committee chairmen but did not give them a breakdown of the calculations. Members of the state Medicaid Innovation and Reform Commission have also been briefed.

The proposal to expand Medicaid, an option for states under the Affordable Care Act, could add 400,000 additional uninsured Virginians to the rolls of the federal-state health-care program for the poor. In addition, the expansion would funnel payments to hospitals that, under other provisions of the law, are no longer reimbursed for some charitable care of the uninsured.

About half the states have opted to expand Medicaid.

Officials in the state Department of Medical Assistance Services have been working on the numbers since last summer, and Hazel said neither the timing nor the estimate had anything to do with current political negotiations over Medicaid.

“We have been working on these numbers for a long time,” said Hazel, who was appointed health secretary in 2010 by Gov. Robert F. McDonnell (R) and retained by McAuliffe. “It serves no purpose to try to play with the numbers.”

Hazel told reporters Wednesday that he was surprised by the amount of savings in the new estimate, which includes data from states that have launched their own Medicaid expansions. Understanding of the health-care law has evolved over time, he said, along with data about the uninsured population.

The savings come from higher estimates of how many indigent patients would newly qualify for Medicaid, as well as better estimates of how much their care would cost, according to state officials. The prior estimate, issued in 2012, was conservative, the officials said, because not as much was known about how a Medicaid expansion would work.

The estimate assumes a Medicaid expansion that begins July 1, 2014. Should the expansion begin in October, the state would still save $984 million, officials said. That number would drop to $938 million if the expansion launched at the beginning of 2015.

Jones has asked for an estimate if the expansion was to begin in July 2015, the earliest he says it could realistically launch given the opposition among Republicans to moving this session.

Under the new estimate, Medicaid expansion would begin to cost the state money in about 2021 as federal support declines. Under the Affordable Care Act, the federal government would pay 100 percent of expansion costs for the first three years and has pledged to pay at least 90 percent thereafter. Sen. Walter A. Stosch (R-Henrico), chairman of the Senate Finance Committee, has proposed that any savings from an expansion be banked to pay for those future costs.

Cynthia Jones, director of the Department of Medical Assistance Services, sent a letter to the Medicaid Innovation and Reform Commission explaining the new estimate. The commission was created last year during the McDonnell administration to investigate the financial impact of expansion and to oversee any reforms.

McAuliffe is pushing for the authority to expand Medicaid if the commission does not act this session. But Republicans have made clear that they have no intention of acting that quickly on what they see as a dangerous embrace of President Obama’s health-care policies.