In interviews and private conversations with more than half of the 45-member Senate Republican Conference, there is a split over a potential McConnell successor. His top deputy, John Cornyn of Texas, is favored to succeed him, several GOP senators said. But others ranging from John Thune of South Dakota to Tennessee’s Lamar Alexander — or a dark horse — are among those who could get serious consideration in the event of a leadership vacancy…

There also appears to be concern among a handful in the Republican Conference that a Minority Leader Cornyn would be hamstrung by the whims of his fellow Texan and conservative firebrand Ted Cruz, pulling the party further to the right…

Aside from Cornyn, GOP senators are privately floating a number of other senators to succeed McConnell, including Thune, the Senate Republican Conference chairman, GOP Policy Chairman John Barrasso of Wyoming and Missouri’s Roy Blunt, the No. 5 in Senate GOP leadership.

Moreover, other rank-and-file Republicans have been suggested as potential McConnell successors, including Alexander and Burr himself.