People who would benefit have little idea what they may lose if Supreme Court strikes down health law.

SEWANEE, Tenn. — As Robin Layman, a mother of two who has major health troubles but no insurance, arrived at a free clinic here, she had a big personal stake in the Supreme Court’s imminent decision on the new national health care law.

Not that she realized that. “What new law?” she said. “I’ve not heard anything about that.”

Layman was one of 600 people who on a recent weekend came from across southeastern Tennessee for the clinic held by Remote Area Medical, a Knoxville-based organization that for two decades has been providing free medical, dental and vision care in underserved areas. Most everyone had spent the night in their parked cars, to get a good spot in line. Daybreak found them massed outside the turreted stone gymnasium of the 150-year-old college, the University of the South, some still wearing pajamas or wrapped in blankets, waiting quietly for the 6 a.m. opening of the doors.

It was Remote Area Medical’s 667th clinic. But this one came at an unusual moment: as the Supreme Court deliberates whether to uphold the health care law that will have a disproportionate impact on the sort of people served by the organization.

Layman was hardly the only patient unaware that the law aims to help people like her, by expanding health insurance beginning in 2014. And this gets to the heart of the political dilemma for Democrats: Despite spending tremendous political capital to pass the law, the party is unlikely to win many votes from the law’s future beneficiaries, most of whom live in Republican-dominated states in the South and West. In fact, many at the clinic said they don’t vote at all.