The correct answer is: “But I have never done that for this reason: I have found that there are so many deserving stenographers and secretaries in Washington that needed the work that I just didn't feel it was right to put my wife on the pay roll.”
Indeed, a red-herring is a statement that deflects attention from an issue to another issue of unrelated importance. In this case, no-one had accused Nixon of putting his wife in the payroll and he knew it. However, he decides to use this point to divert attention from him and focus it on his political opponent, who allegedly did put his wife on the payroll.
