The nomination of Mr. Scalise, 58, who has been the No. 2 leader in the chamber, was a vote of confidence for a deeply conservative Republican who once described himself, according to a local columnist, as “like David Duke without the baggage.” He represents the Louisiana congressional district that elected Mr. Duke, the former Ku Klux Klan leader, to the State Legislature in 1989. His conservative governmental philosophy, the columnist wrote, was not much different from the one Mr. Duke embraced as a politician, including oppositions to taxes and social safety net programs.
Mr. Scalise apologized in 2014 for having attended a white supremacist gathering more than a decade earlier, saying that he had not known the nature of the group.
On Wednesday, Representative Nancy Mace, Republican of South Carolina, cited that episode as a reason not to support him, saying that she would back Mr. Jordan instead.
“I personally cannot, in good conscience, vote for someone who attended a white supremacist conference and compared himself to David Duke,” she told CNN.
In Congress since 2008, Mr. Scalise was diagnosed with blood cancer over the summer and is now undergoing intense treatment, which has prompted him to wear a mask to vote on the House floor and to attend news conferences. And in 2017, during a practice for a congressional baseball game, an anti-Trump extremist shot and seriously wounded Mr. Scalise. He still walks with a limp.
Over the past year, Mr. Scalise has been marginalized by Mr. McCarthy, who has privately described him to colleagues as ineffective, checked out and reluctant to take positions, and cut him out of all major decision making. Their icy relationship made it more difficult for Mr. Scalise to consolidate support in the badly fractured Republican conference.
Catie Edmondson, Robert Jimison and Carl Hulse contributed reporting.