House Majority Leader Kirk Cox (R-Colonial Heights) delivers a resolution Thursday to the Virginia Senate calling for an extension of the current session by 30 days. (Steve Helber/AP)

With two days to go before they are supposed to leave town, House Republicans and Gov. Terry McAuliffe showed no signs Thursday of budging in their standoff over expanding Medicaid, bringing Virginia closer to a historic budget stalemate.

McAuliffe (D) continued making his case on behalf of expansion, accusing Republican opponents of ignoring those Virginians who stand to benefit the most from the program. Recounting wrenching stories from a tour of a health clinic in rural Wise County, the governor said: “Folks, this is about life and death. It is not a partisan political game.”

House Republicans countered by questioning what they described as the governor’s highly political rhetoric.

“This is nothing more than political posturing on his part,” said Del. S. Chris Jones (R-Suffolk), chairman of the House Appropriations Committee.

House leaders also voted to extend the legislative session for 30 days, setting a firm deadline to resolve the Medicaid impasse. They also want to pass the state budget before moving on to the Medicaid question. But both ideas were rejected by the Senate, where a bipartisan majority supports expanding the federal health program for the poor — and where inclusion of the proposal in the state budget is viewed as a major leverage point.

It remains unclear who will blink first and what a final agreement might look like — and whether McAuliffe and lawmakers will pass a budget in time to avoid a shutdown of government services. Although the General Assembly has until the eve of July 1 to avert a shutdown, a major delay in negotiations could gum up local governments and school districts that depend on an early glimpse of the details to plan their spending for the coming year.

McAuliffe has been in frequent contact with the Senate Republicans who crafted the plan to spend $1.7 billion a year using taxes collected in Virginia under the Affordable Care Act to purchase private insurance for up to 255,000 people without health coverage. He has urged them to stand tall against opponents of expansion.

But House Republicans continued to warn that Medicaid costs are soaring even without expansion and threaten to crowd out education and transportation funding if the program is not changed before any expansion is considered.

McAuliffe and top administrators of Virginia’s Medicaid program on Thursday trumpeted what they billed as a major reform to address one of the big demands of House Republicans.

The change, which was launched at the beginning of the month, is intended to reduce wasteful spending and improve care for impoverished disabled and elderly residents who qualify for both Medicaid and Medicare.

The new system is designed to serve up to 78,000 people. If half that number take advantage of it, it will save $126 million in Virginia over two years, administration officials said.

Virginia’s system becomes one of just three such programs nationwide, said McAuliffe, who cited it as proof that the commonwealth is serious about reform — and prepared to add hundreds of thousands more people to the Medicaid system.

“We are now ready to take the next step,” McAuliffe said.

“The General Assembly has put up one false roadblock after another in order to delay the closing of the coverage gap,” he said, a reference to the slice of the population that earns up to 138 percent of the federal poverty level of $11,670 for an individual and would be covered under Medicaid expansion.

Republicans applauded the reform efforts but said they still want to wait and see the results before pulling the trigger on a major expansion.

In an interview, McAuliffe described the struggling patients he met in southwest Virginia, where poverty rates are high, the number of people insured is low and conditions such as diabetes are common. He talked about the challenges facing the nurse practitioner, Teresa Gardner, who heads the Health Wagon group of free clinics he visited.

“She said, ‘People are dying because we can’t provide care for them. We are turning people away,’ ” McAuliffe said. “I’ve moved past probably disappointment to anger that these people are being treated like this. They can get coverage. We can save lives . . . by bringing these billions of dollars back” to Virginia, McAuliffe said.

As McAuliffe walked away from the Wise clinic, he said an older man approached him, grabbed his sleeve and stopped him, causing a brief concern among staffers. The man, who has a daughter in college, described losing his job in a coal mine, running out of unemployment benefits and having no health insurance, McAuliffe said.

“He said: ‘I’m ruined. Do something for me. Help me.’ I said I’m trying. You just feel like you’re helpless,” McAuliffe said.

McAuliffe’s comments drew a quick response from Republicans.

“People currently get service. They’re not dying,” said House Majority Leader M. Kirkland Cox (Colonial Heights.) “That’s the most over-the-top statement I’ve ever heard.”

Del. Jimmie Massie III (Henrico) said helping those who can’t help themselves is a core service of government.

But Virginia has to be cautious about Medicaid expansion. “This is a huge decision, a 10-, 20-, 30-, 40-, 50-year decision. We need to be circumspect about it and get it right,” Massie said.

Pending a decision on Medicaid, the people of Wise can get care, Massie said. Other Republicans noted that they have proposed increasing spending on free clinics, other health centers for low-income residents and hospitals.

“Those people might not have health insurance, but they have access to health care. It’s not the most efficient way to do it, but they have access to emergency rooms,” Massie said. “They have to be treated. We’re treating them. That’s going to be the stopgap in the meantime.”

Gardner, the executive director of Health Wagon, said in an interview that job losses in the coal industry and other economic challenges have boosted the number of clients her clinics see by more than 70 percent since 2012, to 4,167 patients this year. A hospital that had been a major funder is ending its assistance because of its own financial straits. They have a 60-day waiting list. Gardner described attending the funeral of a client’s daughter. The woman, in her 20s, had an abnormal pap smear but lost her insurance and did not follow up. By the time she had some abdominal pain checked out several years later, the cervical cancer had metastasized, Gardner said.

“She shouldn’t have to die of something that probably was preventable if she only had health insurance,” Gardner said.

Gardner said free clinics across Virginia, including her own, see only a portion of the people who actually need help.

“People die when they cannot get into our clinic, they really die,” said Gardner. Many of the people they do see are “train wrecks” by the time they make it in, she said, adding that sometimes pride causes the delays seeking help.

One uninsured client, a 35-year-old man, went without diabetes treatment for so long that he’s blind in one eye and partially blind in the other, she said.

“The diabetes has done so much damage to his blood vessels,” she said. “He suffered heart damage from this.”