Obama has been criticized by some, including Rush Limbaugh, for relying on teleprompters and electronic cue cards when speaking in public. But the extra diligence may now be necessary. For nearly everything he does — bill-signing, urgent matters of statecraft, talk-show palaver — a video record is produced and disseminated at high speed. Obama throws away no appearance, then; he’s almost never caught winging it. He also seems shrewdly mindful that remarks he gives to small groups will find bigger and less predictable audiences online. In his regular YouTube videos, he can be seen first seeking his cue and a camera before holding his head high and maintaining an expression of amused alertness that would bedevil even the most determined digital editors looking later to recast it as anger, sorrow or fatigue.