The claim references Axios reporting on Tuesday that GOP leadership was worried about support for the rule vote. While the evidence confirms Axios reporting on leadership concerns regarding votes, the specific timing ('Tuesday') and the exact nature of the worry regarding 'the rule vote' is derived from the context of the search results, but not independently corroborated by a second source.

The specific details regarding Johnson, Emmer, and McClain persuading defectors, including Greene and Massie, on a specific 'Wednesday afternoon' are not independently corroborated by multiple sources. While evidence confirms the existence and roles of Johnson, Emmer, and McClain, and mentions Greene and Massie, the precise narrative of them being on the floor that specific afternoon attempting to persuade those individuals is only present in the context of the provided web search results, lacking independent confirmation from multiple sources.

The claim that 'Several moderates were also withholding their votes but ultimately backed the rule after conversations with leadership' is mentioned in the context of general leadership tensions in the web search results, but no single source provides a clear, detailed account confirming this specific sequence of events (withholding $ ightarrow$ conversation $ ightarrow$ backing the rule) for multiple moderates.