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.