Thanks for your reply, dag89! It certainly helps to know I am not the only one in this situation. You expressed exactly how I feel when you said you worry about whether you will stand up to expectations. I don't want to turn down the offer solely for that reason, but it certainly makes me more nervous to accept. I also know a lot of people would kill for this opportunity.
I am trying to decide between a funded masters in mechanical engineering at MIT or a PhD in Robotics at Georgia Tech (I received a fellowship). Any advice on which would be better for getting an industry job in robotics? I realize I could always do the master's at MIT and continue for my PhD later but I am worried about being successful at MIT based on how difficult it is. It might just be impostor syndrome but I am shocked I even got into MIT and would probably be at the bottom of the intelligence spectrum there.