Has the White House Ever Been Involved in Influencing Federal Reserve Policy?

Of course, but you only learn about it decades later.

From a January 27, 1963 talking points memo to President  Lyndon Baines Johnson by then-Chairman of the Council of Economic Advisers Walter Heller on an up-coming meeting by the President with then-Federal Reserve Chairman Bill Martin:

Monetray policy coordination: Martin should connsult with the President and/or his major economic polic advisers before making significant policy changes--he does a good deal of this  now with Treasury, but use of our "Quadriad" group for such coordination would be appropriate.

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Martin should use his influence to achieve some leavening of the boards of directors of the 12 Federal Reserve Banks by at least occasional appointment of New Frontier types to "Class C: directorships--e.g. Jim Tobin or Bob Solow at the Boston Fed. One liberal or moderate really shouldn't threaten the foundations of the Federal Reserve System.  

Tobin ended up a member of the Board of Governors of Federal Reserve System for several terms.

From Managing Macroeconomic Policy: The Johnson Presidency

 -RW