TEXARKANA, Tex. — On a hazy, hot evening here, Janice Marks ate a dinner of turkey and stuffing at a homeless shelter filled with plastic cots before crossing a few blocks to the Arkansas side of town to start her night shift restocking the dairy cases at Walmart.

The next day, David Tramel and Janice McFall had a free meal of hot dogs and doughnut holes at a Salvation Army center in Arkansas before heading back to their tent, hidden in a field by the highway in Texas.

None of the three have health insurance. But had Ms. Marks, 26, chosen to sleep on the side of town where she works, or had Mr. Tramel and Ms. McFall, who are both in their early 20s, made their camp where they had eaten their dinner, their fortunes might be different.

Arkansas accepted the Medicaid expansion in the Affordable Care Act. Texas did not.

That makes Texarkana perhaps the starkest example of how President Obama’s health care law is altering the economic geography of the country. The poor living in the Arkansas half of town won access to a government benefit worth thousands of dollars annually, yet nothing changed for those on the Texas side of the state line.

After the Supreme Court decided in 2012 that states could not be compelled to expand Medicaid to cover more of their low-income residents, many politicians voiced fears that the poor in states that opted out of the expansion might flood into states that opted in.

Thus far, 26 states and the District of Columbia have chosen to extend Medicaid, encouraged by the promise that the federal government will shoulder 90 percent of the cost indefinitely. The others — including Texas — have so far declined.

But none of the low-income Texarkana residents interviewed realized that moving to the other side of town might mean a Medicaid card. In fact, health researchers and those who work with the poor expect very few Americans to move between states to take advantage of the law.

“It’s impossible to understand what it is to move when you have nothing,” said Jennifer Laurent, the executive director of Randy Sams’ Outreach Shelter, where Ms. Marks is staying until she puts together enough savings from her two low-wage jobs to find her own place. “To risk everything — losing your bed, your sense of community — for an uncertain benefit? There’s no way you want to risk that.”

Research on other expansions of government benefits has borne that out: A study in the journal Health Affairs looked at the “welfare magnet hypothesis” and found no evidence that it exists.

“I’m sure, anecdotally, that some people will move,” said Benjamin Sommers, an assistant professor of health policy and economics at the Harvard School of Public Health and a co-author of the study. “But is this a major budget issue for states expanding Medicaid? Will there be a major wave of people moving to get insurance? Probably not.”

The disparities among states have left about eight million low-income adults ineligible for Medicaid and have widened the difference in what federal safety-net benefits are available to similar families in different states. There are a number of border communities where one state is expanding Medicaid and the other is not: West Memphis, Ark., and Memphis; Chicago and Gary, Ind.; Washington’s Maryland suburbs and those in Northern Virginia; and Spokane, Wash., and Coeur d’Alene, Idaho.

Perhaps nowhere is the anomaly clearer, though, than in two-state Texarkana. This close-knit community, with about 66,000 residents altogether, has two mayors, two fire departments and two police departments. The Texas side is dry; liquor stores abound on the Arkansas side. And every autumn, the fierce high school rivalry between the Texas Tigers and the Arkansas Razorbacks flares anew.

“We’re an odd little area down here,” said Prissy Hickerson, a Republican who represents Texarkana in the Arkansas House of Representatives.

Both sides of Texarkana are largely middle and lower-middle class; its major employers are big-box stores, hospitals, chicken-processing plants, an Army depot and a tire factory. But unlike much of energy-rich Texas, it has seen its economy stagnate in recent years. Ms. Laurent said she struggled to meet more need with less money; grants and donations to the shelter dropped sharply last year.

For the town’s lowest-income residents, finding health care is one more hardship. Ms. Marks had a hole in her tooth this winter, she said, and went to the emergency room. They gave her a painkiller and a bill for $600, which she has ignored. The tooth remains so damaged that she can chew on only one side of her mouth.

“I know it’s past due,” she said in response to the letters the hospital has sent her. “But I can’t just pay y’all $600. I don’t have $600.”

Another resident at the Randy Sams’ shelter, Ed Miller, 42, has congestive heart failure and sleep apnea. Recently, he went to the hospital and received a diagnosis of bronchitis too. Asked if he would consider moving to Arkansas to gain access to Medicaid, he responded, “I might look into that.”

The shelter helps its residents gain access to the government programs they are eligible for: food stamps, Social Security, disability, housing vouchers when available. Once, Ms. Laurent said, an Arkansas social worker came across the state line to see if anyone might be eligible for the Medicaid expansion.

But even many qualified people resist using government services, because of fear, a lack of knowledge or a criminal conviction. “They just don’t trust the government,” Ms. Laurent said. “They’ve been told no over and over and over again.”

And moving even a few blocks away might pose an insurmountable challenge. The Salvation Army shelter on the Arkansas side of town charges $6 a night, more than many of the very poor can afford. Randy Sams’, on the Texas side, is free.

“I tell my clients: You’ve got to have paper, or you’ve got to have paper,” Ms. Laurent said. “You’ve got to have money, or you’re going to have to fill out a lot of paperwork for benefits.”

Mr. Tramel said he walked to Texas from Missouri, finding God and kicking a drug habit along the way. The trip took him 11 days. He has no Social Security card, birth certificate or driver’s license, let alone a stable address. The paperwork challenge of establishing residency in a state and applying for benefits, he said, seemed overwhelming to him.

“Medicaid, I think that should be universal,” he said, getting ready for the long walk back to his tent.

Indeed, until the Supreme Court ruling, the Obama administration had intended for the Medicaid expansion in the Affordable Care Act to be universal, covering all adults earning up to 133 percent of the federal poverty line, about $15,500 annually for a single adult or $32,000 for a family of four.

That’s the way it is working out on the Arkansas side of the border, where health clinics and social service agencies are signing up eligible residents, even though this corner of the state is largely Republican and broadly resistant to the health care law.

The expansion is already having an effect on the city’s biggest provider of charity care, the nonprofit Christus St. Michael Health System. “We’re seeing more patients with a payer,” said Chris Karam, its president, referring to those with health insurance coverage.

On the Texas side, though, it’s business as usual. “It makes me mad,” said Mr. Miller, who is not receiving any federal benefits at the moment despite his array of illnesses. “They need to quit playing games with people’s lives. Rich people. Government people.”