GOP lobbyist Jeff Miller, one of McCarthy’s closest friends and biggest fundraisers, and Brian O. Walsh, a Republican strategist who works for multiple McCarthy-backed groups, were both involved in an independent effort to oppose Cawthorn as part of a broader project to create a more functioning GOP caucus next year, said the Republicans, who like others spoke on the condition of anonymity to discuss private conversations.

Targeting Cawthorn was part of a larger behind-the-scenes effort by top GOP donors and senior strategists to purge the influence of Republican factions that seek disruption and grandstanding, often at the expense of their GOP colleagues. The political machine around McCarthy has spent millions of dollars this year in a sometimes secretive effort to systematically weed out GOP candidates who could either cause McCarthy trouble if he becomes House speaker or jeopardize GOP victories in districts where more moderate candidate might have a better chance at winning.

The allies close to McCarthy have sometimes taken steps to conceal their efforts, as they did in the Cawthorn case, with money passing from top GOP donors through organizations that do not disclose their donors or have limited public records, federal disclosures show.

In safe Republican districts, controversial Republicans like former New York State party chair Carl Paladino, Florida state Rep. Anthony Sabatini and…