Twice a year, Tennessee holds a “health care lottery” that gives some hope to the uninsured residents in the state who can’t afford health coverage. Tennesseans who meet certain requirements — in addition to falling below a certain income threshold, they must be elderly, blind, disabled, or a caretaker of a child who qualifies for Medicaid — may call to request an application for the state’s public health insurance program, known as TennCare.

The lottery is part of TennCare’s “spend down” program, which allows a resident’s income to be calculated after subtracting their medical costs from their total earnings. That means that some Tennesseans who technically earn too much annual income to qualify for public insurance could still be eligible for TennCare if they successfully complete the application process. The New York Times notes that while other states have similar “spend down” initiatives, most don’t limit the lottery enrollment period to a narrow window of call-ins. The unique enrollment process in Tennessee highlights the overwhelming demand for affordable health services, as many low-income Americansfall into a gap between being able to qualify for Medicaid and being able to access private insurance coverage:

State residents who have high medical bills but would not normally qualify for Medicaid, the government health care program for the poor, can call a state phone line and request an application. But the window is tight — the line shuts down after 2,500 calls, typically within an hour — and the demand is so high that it is difficult to get through.[…] “It’s like the Oklahoma land rush for an hour,” said Russell Overby, a lawyer with the Legal Aid Society in Nashville. “We encourage people to use multiple phones and to dial and dial and dial.” The phone line opened at 6 p.m. on Thursday for the first time in six months. At 5:58, Ida Gordon of Nashville picked up her cordless phone and started dialing. Ms. Gordon, 63, had qualified for TennCare until her grandson, who had been in her custody, graduated from high school last spring. Now she is uninsured, with crippling arthritis and a few recent trips to the emergency room haunting her. “I don’t ask for that much,” Ms. Gordon said as she got her first busy signal, hanging up and fruitlessly trying again, and then again. “I just want some insurance.”

If Tennessee Gov. Bill Haslan (R) opted to expand Medicaid under Obamacare, more than 180,000 people would be able to be added to the TennCare rolls by 2019. Obamacare’s Medicaid expansion would extend coverage to low-income Americans whose earnings are above the current cut-offs for public assistance — which would include many of the people like Ida Gordon, who are desperately dialing and redialing in the hopes of winning an elusive health care lottery. Haslan has not yet decided whether Tennessee will accept Obamacare’s optional expansion of the Medicaid program, although he has indicated that he may make his decision sometime this week.

A growing number of GOP governors across the country have begun to concede thatexpanding Medicaid makes sense for the low-income residents in their states. But many of their fellow Republicans still aren’t willing to cooperate with the health reform law whatsoever — even going so far as to suggest that Obamacare will “degrade” or “destroy” what is already the “best health care system the world has ever known.” As Tennessee’s health care lottery demonstrates, however, the low-income Americans who are resorting to desperate measures to access the care they need may not agree with that assessment.