I learned this expression today while repeating one of my favorite stories about Bebel, or Maria Isabel, my niece. She's just turned five. One night we were at dinner with her and a bunch of other family members. Someone commented that Bebel falta educação, that is, she lacks manners. Wanting to try out my Portuguese, I turned to her and, with a mouthful of french fries, said, "So, you don't have manners, Bebel?" Without missing a beat, she rolled her eyes and and with an exasperated sigh, replied, Não falo com boca cheia -- "I don't speak with my mouth full."
My forehead is still bleeding from that one.