As the 2022 elections approached with some Republican Senate candidates on the ropes, Senator Mitch McConnell was already looking ahead to 2024. He saw opportunity in the person of Jim Justice, the popular Republican governor of West Virginia whose term would — fortuitously for Mr. McConnell — end in 2024.

“Here we had a guy who was term-limited and who everybody assumed was going to just go off into the sunset,” recounted Mr. McConnell, the Kentucky Republican and minority leader. “But he had to-die-for numbers.”

Mr. McConnell secretly flew to West Virginia on Oct. 19, 2022. Over lunch at Governor Justice’s home, he tried to interest him in running for Senate. In April 2023, Mr. Justice announced he would seek the seat held by Senator Joe Manchin III, probably the only Democrat with any chance of winning in super-red West Virginia.

In November, Mr. Manchin announced he would not seek re-election. Earlier this month, Governor Justice won his primary, putting him squarely on track to capture the Senate seat, which would leave Republicans just one seat shy of a majority.

“I’m pretty sure, barring some intervention, that’s No. 50,” said Mr. McConnell, referring to the number of seats his party would control if all went according to plan. Democrats would need to hold everything they now have in the 51-to-49 Senate or pick up a Republican seat to stay in the majority next year, he noted. “They’re left with trying to have a perfect score.”

Though Mr. McConnell is stepping down from his leadership post in 2025 and is widely expected to retire when his term ends in 2027, he is determined to leave his successor with a majority in the Senate after heading his party in both the minority and the majority over almost 18 years. His personal effort to recruit Governor Justice was a central element of his plan.