BROOKINGS, S.D. — First came the Republicans, all smiles and matching blue T-shirts as they marched in this college town’s annual Hobo Day homecoming parade. Then the tractor team rolled past, and the dairy club, and the Corn Palace Shriners.

Finally, at the end of the line: the Democrats. Behind as usual.

Farmers and ranchers from this rural state once sent liberal icons like George McGovern to Congress, but these days, Democrats have all but vanished into the plains, a stark example of how far the party has tumbled in rural America. They hold no statewide elected offices in South Dakota. They make up less than 20 percent of the State Legislature. Their numbers are shrinking so fast that they rank below registered independents in a dozen counties.

But on a sunny Saturday, shaking hands and nudging his wheelchair up the parade route, came Billie Sutton, a 34-year-old state senator and onetime rodeo rider who is making a surprisingly competitive run for governor against South Dakota’s four-term Republican congresswoman, Kristi Noem.

Mr. Sutton is running as an anti-abortion conservative Democrat with cowboy cred and a stirring life story. His supporters think he can show Democrats how to start rebuilding the party in socially conservative states where the ag-heavy economy rises and falls with rain cycles and soybean prices.