JACKSON, Miss. — Inside an abandoned grocery store-turned-church here, a dozen black pastors gathered to discuss a seemingly impossible task: persuading their congregations to vote Republican next week.

“In tough times, you’ve got to do some unusual things,” said Bishop Ronnie C. Crudup Sr., a pastor of the New Horizon Church International in Jackson.

Unusual is an understatement. Mississippi, with its painful history of Jim Crow laws, may have the most racially polarized electorate in the country. Blacks make up a higher percentage of the electorate here than in any other state — 36 percent in 2012, according to exit polls. But they are so overwhelmingly Democratic that they remain nearly invisible in Republican politics, with just 2 percent participating in the Republican primary in 2012.

Now, with Thad Cochran, the state’s senior Republican senator, fighting political extinction in next Tuesday’s primary, his campaign is taking the unlikely step of trying to entice black voters to help decide the most high-profile Republican contest in the country.