I looked into that. Not possible for several reasons.

1. Color of building is white/gray, while the reflection is reddish/brown
2. The height of the building does not match the # of stores While the first 2 can be explained by refraction and maybe pitch of camera, however, the most most important one is the actual direction the photo was taken. Let me explain; The picture taken is obviously of the west wing, where the press room is. If you look at the west wing floor-plan, you would see that the reflection would be pointing to North side of the west wing while the building you are referring to is located on the west side of the building. To make that shot work (ignoring color and height of the building) you would need a mirror set at 45 degrees aimed to the south west. Add to that: there should be at least 2" of snow according to weather report, while the shot taken shows clear skies and no snow. Working on it still though, I went in trying to disprove the photo (hoping that I was wrong), but the things I explained to you show there is something not adding up.

Edit: Its actually the building on the North West accross the street from the west wing/garden. Seems like its the actual WH boys.