The proposed motion, to be presented to the 168-member RNC at its annual winter meeting in Honolulu at the end of this month, also would direct him to donate to the RNC and Republican candidates all proceeds from the book.

A storm of criticism has swirled around Mr. Steele over his missteps, retractions, and profiting from speeches and his new book, “Right Now: A 12-Step Program for Defeating the Obama Agenda.” Three of his predecessors have publicly castigated his actions. His critics say the controversy is distracting voter attention from the Democrats’ problems 10 months before midterm elections…

But in another sign of internal tension, Mr. Steele’s supporters have begun citing the precedent of Mississippi Gov. Haley Barbour, e-mailing to members a claim that Mr. Barbour was guilty of the same things Mr. Steele is now being criticized for doing when he headed the RNC in the mid-1990s, The Times also has learned.