The man whispering to Bush is Andrew Card, his chief of staff. Bush had been told before entering the school that a plane had hit the World Trade Center. This was just a few minutes after the first impact, and apparently Bush was told that it had been a small plane and appeared to be an accident. He figured it was no big deal and began speaking to the class.
In the exchange shown in the picture, Card told Bush that a second plane had struck and that it looked like a terrorist attack. Bush spoke to the class for a few more minutes, made a brief public statement (the one in which he referred to the "folks" who had carried out the attacks), and then left for AF1.
"Let me think about it" = the coward's way of saying "no"