I’ve been visiting LibriVox lately, first as someone interested in free audio books and then as someone interested in recording audio books for free. As one of my first contributions, I recorded a very short 1962 sci-fi story that takes the form of teletype messages between the WH and “Pacific Space Command.” The collection isn’t done yet, but my part is available. (Don’t worry, I didn’t try to emulate JFK’s accent for the WH end of the communications.)
Of course, everything recorded must be public domain, but so far all I’ve found that interests me in terms of WH material is TR’s letters to his children. I suppose most presidential speeches are public domain, but can anyone think of something more closely related to the White House? Ike Hoover’s memoirs would be fun, but I don’t think they’ve fallen out of copyright (everything before 1923 is PD and anything until that wasn’t renewed after 28 years is PD; more recent stuff has different protection).
UPDATE: After another quick search, I think I might do Herbert Hoover’s wildly-optimistic 1929 State of the Union address, altho it’s rather long (they got much shorter later on).