There are two phone numbers in the Times photo above; we've partially blurred them, but they are legible in the original, part of a slideshow about the president's speech to a joint session of Congress tonight. The first is formatted 6-XXXX, indicating it is likely an internal number inside the White House's 202-456-XXXX circuit. The second number has a Chicago area code, indicating perhaps a cell phone originally issued by the campaign.
Judging from the "Favreau/Rhodes" notation above the numbers, they would appear to correspond to Favreau, 27-ish, and/or his fellow young gun Ben Rhodes, a 30-year-old foreign policy speechwriter.
In all likelihood, the Times was trying to throw together comprehensive coverage on deadline and let the numbers slip through. Hardly an unforgivable lapse. But given the ongoing national celebrification of what were once relatively unsexy White House jobs — assistant, social secretary, speechwriter, chief of staff — the newspaper should probably be more careful with what seems like presidential detritus. There is no shortage of people rifling through the administration's multimedia dregs.