They proudly say that they comply with federal privacy law, eschewing cookies, but sneakily use Addthis's "canvas fingerprinting," a product whose other major user is Youporn (but they stopped after they were outed, and the White House didn't).
The original research comes from a team at KU Leuven and Princteon, and was published by Pro Publica. The researchers found that the White House had deployed Addthis's spyware cookies — which are not blocked by browsers, even when tracking is turned off — on every page, even on the privacy policy page which trumpets that the site isn't using any tracking.
EFF's explainer for this is a good and accessible piece, and includes the recommendation to try out Privacy Badger to block canvas fingerprinting; you can also use plugins like Noscript.
White House Website Includes Unique Non-Cookie Tracker, Conflicts With Privacy Policy
[Peter Eckersley and Kurt Opsahl/EFF]
(Image: Mystery Eyeball, Florida Fish and Wildlife, CC-BY)