Ha I did the same thing too! Knowing me, I would have waited even later, but the deadline was the day before my thesis was due. Coincidentally, get my thesis comments back tomorrow... WHY does Fulbright have to work with my department to make my life so freaking stressful?!?
I agree on the unsettling bit, but my bet is they at least save some spots for exceptional people who turn their applications in exceptionally close to the deadline. Or, MA postal service blows. Let's hope for the latter.