Terry McAuliffe has made Medicaid expansion central to his bid for governor, saying it would provide health insurance to 400,000 needy Virginians, create thousands of jobs and provide the state with a $2 billion a year windfall.

Some Republicans say his push to expand the health-care program could lead to something less appealing: a government shutdown.

“I will not sign a budget in Virginia unless it includes the Medicaid expansion,” McAuliffe said this summer in an interview with AARP. He made a similar comment at a dinner with Loudoun County Democrats, the Loudoun Times reported in June.

Given overwhelming opposition to expansion in the GOP-dominated House of Delegates, that campaign promise amounts to a threat to hold the state budget hostage to McAuliffe’s Medicaid goal, some Republicans say. Critics say it also shows that McAuliffe, who has billed himself as a bipartisan consensus builder, would take a highly partisan, autocratic approach to governing.

“Terry McAuliffe wants to paint himself as a bipartisan problem-solver, but he’s already drawing red lines and threatening Washington-style government shutdowns here in Virginia,” said House Speaker William J. Howell (R-Stafford).

McAuliffe’s campaign said he was not threatening a shutdown, just expressing the importance he places on expansion.

“Medicaid expansion is a top priority for Terry and a goal shared by mainstream Republicans in Virginia and across the country,” McAuliffe spokesman Josh ­Schwerin said in an e-mail. “Nobody is arguing for a government shutdown. Terry hopes to work in a bipartisan way to get this mainstream accomplishment done.”

Under the federal Affordable Care Act, states have the option to open their Medicaid programs to people with incomes that are up to 138 percent of the national poverty level — about $32,000 for a family of four — with the federal government paying the entire cost for the first three years. The federal share gradually declines to 90 percent. Virginia would initially receive about $2 billion a year from Washington if it expands the program, which serves the poor, elderly and disabled.

Some Republicans, including Gov. Robert F. McDonnell and Attorney General Ken Cuccinelli II, who is running against McAuliffe, doubt that Washington has the money to make good on that promise.

The politics of Medicaid expansion have not always broken neatly along partisan lines in Virginia, where moderate Senate Republicans favor expansion, or across the country, where some conservative Republican governors have opted to take the money. But the issue reveals one of the starkest contrasts between McAuliffe and Cuccinelli.

McAuliffe supports expansion for its own sake and also invokes the money it is expected to save the state. When asked how he would bankroll his broader platform, which includes higher teacher pay, lower college tuition and more spending on pre-K and K-12 education, he often cites the Medicaid money.

Cuccinelli, on the other hand, was the first attorney general in the nation to sue the federal government over Obamacare. Even after his suit was thrown out in 2011 and the U.S. Supreme Court upheld the law in a different case, he pledged to fight on.

“Under current law, Medicaid expansion would have significant negative economic consequences for Virginia,” campaign spokesman Richard Cullen said in an e-mail. “There’s no conceivable way that the federal government will live up to its end of the bargain with Medicaid expansion. As Governor, Ken will work with Democrats and Republican legislators on significant reforms that ensure Medicaid recipients have access to high quality care and as much flexibility as possible.”

Democrats in Virginia’s legislature played hardball with Medicaid expansion early this year, vowing to defeat a landmark $1.4 billion-a-year transportation package — McDonnell’s top priority — unless he agreed to a deal on Medicaid. It called for expanding the health-care program if Washington agreed to reform the way it is run in Virginia.

McDonnell and an even more reluctant House accepted that deal in February, creating a commission that has begun meeting and monitoring progress on the sought-after reforms. As Democrats celebrated that seeming victory, McDonnell and fellow Republicans opposed to Obamacare said that the deal would make it harder to expand Medicaid because the decision would lie with the GOP-dominated commission, not the next governor.

But regardless of what the commission decides, people on both sides of the debate generally agree that the next governor could try to bypass the panel by deciding whether to include the federal Medicaid money in the state budget. The hurdle then would be to get the General Assembly to go along with that budget.

If it includes Medicaid expansion, that could be a tall order in the House, where Republicans are not expected to lose their overwhelming majority in this year’s elections.

“The House has very strong reservations about Medicaid expansion,” said House Majority Leader M. Kirkland Cox (R-Colonial Heights). “It’s certainly not something the House has favored in the past, so to draw that line in the sand at this point is problematic.”

House Minority Leader David Toscano (D-Charlottesville) said “horse trading” might sway some Republicans. He praised McAuliffe for vowing to make Medicaid expansion part of any budget he signs.

“I think it’s great that he’s doing it because he’s laying down a marker,” Toscano said. “He’s saying uncategorically that this is a priority. . . . McAuliffe is attempting to lead. He believes, as I do, that this should not be a partisan issue.”

Lt. Gov. Bill Bolling (R), who dropped out of the race for governor early this year, has endorsed Medicaid expansion. He said the General Assembly will have to find a compromise.

“I think both sides are just doing a little political posturing on this issue, staking out their respective positions,” Bolling said. “Most Republicans in the House of Delegates don’t want to expand Medicaid, but Senate Democrats and some Senate Republicans do. The political realities of a divided legislature will ultimately force both sides to give a little bit to reach an agreement. I think Mr. McAuliffe understands that.”