My husband had an unexpected business trip to London this summer. He booked his trip, made an appointment at the passport center in Stamford CT for a Friday, we went tot he appointment on Friday, he got the passport in the mail on Tuesday and he traveled the following Friday. They told him that if he was traveling within 48 hours of his appointment, he would have walked out of the passport center with his passport in hand. Of course each level of expediting costs more. I think it cost him about $220 to get his passport.
The bigger issue you might have is needing a Visa, depending on the country you are visiting. That might have to involve a trip to a Brazilian Embassy or Consulate in person once you have your passport in hand.