House of Brain

Ben Alpers charts the rise and fall, from Kennedy through Ford, of"the White House Intellectual-in-Residence" (not that it's existed as a post officially so signified, of course):

The designated White House intellectual-in-residence may have marked a particular moment in the American presidency. Kennedy, Johnson, Nixon, and Ford had very different relationships with and attitudes toward intellectuals in general. Kennedy cultivated them. Johnson and Nixon could be quite hostile to them. Ford quite indifferent. But each felt the need to maintain this peculiar institution created by JFK. And their predecessors and successors—many of whom encouraged more active dialogue between intellectuals and the White House—did not.

What distinguished these four presidencies was not, then, a shared, positive attitude toward intellectuals. The phenomenon of the White House intellectual-in-residence may have, instead, been a kind of apotheosis of the celebration of expertise in post-war American political culture. White House intellectuals could burnish the court of the imperial presidency. But as both that vision of the presidency and the status of intellectuals—and social scientific experts in general—began to wane, the logic of this never-entirely-logical post faded as well.

Alpers' reflections are inspired by Tevi Troy's book Intellectuals and the American Presidency (New York: Rowman and Littlefield, 2002), which I've got around here somewhere but haven't read.
Alpers also notes that"though Barack Obama has long enjoyed the support of a number of prominent academics and public intellectuals—from Lawrence Lessig to Cass Sunstein to Samantha Power—there’s been no indication that the Obama White House will revive the post created originally for Arthur Schlesinger, Jr."