“It’s significant for this region, and it’s significant for the Republican Party,” said Mr. Byrne, who beat a Tea Party-backed candidate in a special House election in December.

Conservative groups such as Club for Growth, the Senate Conservatives Fund and FreedomWorks and activists such as Sarah Palin, the radio host Mark Levin and the social conservative Gary Bauer have flooded the state, hoping to turn Mr. Cochran into a paragon of big government, then send a signal with his defeat that the Tea Party movement is alive and kicking.

Mr. Cochran’s backers, including the U.S. Chamber of Commerce, every major elected official in the state and former Gov. Haley Barbour, want Mississippi to be the conservative outside groups’ Waterloo. Mr. Barbour is raising money and a nephew, Henry Barbour, a member of the Republican National Committee, is running a “super PAC” established to back Mr. Cochran. Henry’s brother, Austin, is a senior Cochran campaign adviser working with Stuart Stevens, a prominent Republican strategist and Mississippi native.

Mississippi’s power structure is in a bit of a panic. The economically poor state has been rich with powerful politicians in Washington, who have unapologetically protected its military bases and shipyards, built its roads and universities, reconstructed its beachfronts, and dredged its rivers. The state has had only a handful of senators since 1947, including Mr. Cochran, a powerful member of the Appropriations Committee; Trent Lott, a Senate majority leader; and John C. Stennis, whose 41 years of service was marked by military advocacy and the creation of the modern Navy.

On Wednesday, the personal finance social network WalletHub said Mississippi and New Mexico were tied as the states most dependent on the federal government, based on taxes paid versus largess received, federal funding as a percentage of state tax revenue and the number of federal employees per capita.

Since 2010, the Tea Party has largely won the battle for Mississippi’s House delegation, as it has in much of the South. Three of the state’s four House members have come to power under the Tea Party banner.