Senator Mitch McConnell’s second alarming medical episode before television cameras on Wednesday has renewed scrutiny on his health as well as speculation about possible replacements for the longtime leader should he be forced to step aside.

A change at the top would be significant for Senate Republicans, considering that Mr. McConnell has been their leader since 2007 and had been the No. 2 Republican for four years before taking the helm. This year, he became the longest-serving Senate leader in history, a milestone he had long sought.

Mr. McConnell, who won election to a seventh term in 2020, has said he has no plans to leave his post, and so far his colleagues have refrained from pressuring him or jockeying — even behind the scenes — for his spot. But the spate of incidents, including a fall in March and two sudden bouts of momentary paralysis in public, has turned attention to who might follow him.

Topping the list are three leading candidates referred to informally in the Senate as the Three Johns.

Mr. Thune, 62, is the current No. 2 Senate Republican, known as the whip. The affable South Dakotan has held the position since 2019 after his predecessor, Senator John Cornyn of Texas, was forced out by term limits. A former House member, Mr. Thune was elected to the Senate in 2004 by defeating Tom Daschle, then the Democratic leader, in one of the nation’s top Senate races. He is a traditional Republican fiscal conservative who has run afoul of Donald J. Trump for dismissing Mr. Trump’s claims that the 2020 election was stolen from him. Mr. Thune considered retiring from the Senate last year but then easily won re-election. He was the chairman of the Commerce Committee before joining leadership, and he successfully fought to keep Ellsworth Air Force Base open in his home state in 2005 when it was recommended for closure.

Mr. Cornyn, 71, is the former No. 2 Republican in the Senate and a top lieutenant and adviser to Mr. McConnell. He has made no secret of his interest in replacing Mr. McConnell should there be an opening at the top. Outside of leadership, Mr. Cornyn, a former Texas Supreme Court justice and attorney general, has made his mark on the Judiciary Committee, where he is a senior member actively involved in judicial nominations and other legal affairs policy. After the mass school shooting in Uvalde, Texas, last year, Mr. Cornyn was delegated by Mr. McConnell to negotiate with Democrats on new bipartisan gun safety legislation that eventually was approved by Congress despite expectations of failure. He was also a champion of the federal prison overhaul meant to reduce mass incarceration. On the political side, Mr. Cornyn was seen as an effective head of the National Republican Senatorial Committee and has a strong fund-raising record, a fact not lost on his colleagues.

Mr. Barrasso, 71, an orthopedic surgeon, is the No. 3 Senate Republican and is known for his deep interest in energy policy. He was appointed to the Senate in 2007 to fill the vacancy left by the death of Craig Thomas and has been easily elected three times since then. He fits the profile of a Western conservative with his strong pro-gun and property rights stances. Mr. Barrasso has also maintained a good relationship with Mr. Trump, setting him apart from Mr. McConnell and Mr. Thune. Mr. Barrasso is seen more as a candidate for the No. 2 slot if there is a McConnell departure, and his allies believe he would be a good fit there.

Senators Joni Ernst of Iowa and Shelley Moore Capito of West Virginia are also members of the Republican leadership team and would merit some consideration for promotions if there were a shake-up.

Ms. Ernst, 53, is a military combat veteran who serves as the No. 4 leader as chair of the Republican Policy Committee. Ms. Capito, 69, hails from a storied West Virginia political family and is vice chair of the Senate Republican Conference. While popular with their colleagues, both would be very long shots for the top post.

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