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The decision by Senator Mitch McConnell to step away from leadership at the end of the year has thrown Senate Republicans into an extended, potentially disruptive nine-month battle to succeed him in the middle of a presidential race and a campaign for control of the chamber.

A contest that had been simmering in the background was suddenly thrust front and center this week by Mr. McConnell’s earlier-than-expected announcement that he would not seek to remain his party’s leader. The contenders immediately began wooing their colleagues for the chance to become the first new face of their party in the Senate in almost two decades.

“It is a lot of runway,” Senator John Thune of South Dakota, the No. 2 Republican, said about the months remaining before the party’s first seriously contested leadership race since Mr. McConnell took over in 2007. “But it is what it is. So you just have to adapt.”

Congressional leadership contests are the most inside of inside games on Capitol Hill, with the secret-ballot outcomes determined by personal relationships, grudges and who lawmakers see as the best option for their own ambitions as much as serious policy positions or the state of the institution. The true electorate is not even known yet, since those voting for next year’s leader will include anyone who wins a seat in November — and exclude anyone who loses.

That reality was underscored on Friday morning when Senator John Cornyn of Texas, the former No. 2 Republican, enthusiastically endorsed Kari Lake, the Republican front-runner in Arizona’s Senate race. Mr. Cornyn, the only one so far to officially announce that he is running, has tried to get off to a quick start in his drive to replace Mr. McConnell, with an all-out push to his 48 Senate colleagues and beyond.

“I’ve called them all,” Mr. Cornyn said in an interview. “I’ve called them all and met with a number of them personally. Most of them say, ‘Well, you know, we’d like to have a more extended conversation.’”