If this very, very poor man’s Snowden wasn’t yet tracked down in person, then it was going to be easy to trace them online.
How to identify the rogue White House tweeter in 3 easy steps
Chris Monteiro

For the record, if the White House really wanted to find out, they’d send the FBI (because part of their charter is handling the civilian side of counter-intelligence investigations) to Twitter and force them to hand over all of the information they had on @whitehouseleaks so they can hunt down the people behind that account. This isn’t really going to put @whitehouseleaks at any more risk then they are now.

Besides, it’s way too creative a solution to the problem for them to consider. They don’t think like this.