The recital piece should be finished (notes and rhythms well-learned) at least two months before the recital date. The remaining time can then be spent polishing execution, completing memory, and honing interpretation. This large "cushion" of time will help the student relax, especially if it is a first recital.
Under no circumstances, I believe, should the teacher assign "a recital piece" to be learned a month before the performance. Students are already nervous enough about the idea of playing in public. If they are assigned to play a piece they must learn in a short time -- and one they might not particularly like once they starting work on it -- they will approach the recital with terror, rather than enthusiasm.
Instead, at least two months before the date, the teacher and student -together- should select a recital piece that the student is already learned (no eleventh-hour scramble!) and which the student enjoys playing. The student generally feels comfortable with the piece already and because he likes it he will be willing to perfect it even further. Further, this piece should be well within the student's grasp to play really well. I don't feel it should be the most difficult piece the student can play or the most recently-learned. In fact, I feel it is far better if the piece is the opposite. It should be a well-worn "old shoe" piece that the student can play with confidence.
Also, the teacher should emphasize that the purpose of the recital is to -share- the music with other the listeners. It is not a time to show off; it is not a final exam. A proper attitude can go a -long- ways toward dispelling the jitters and the competitive urge between students which takes a negative form of one-upsmanship rather than an impetus towards excellence.
You also may be interested in my thoughts on memorization for recitals, adults' fear of playing in public, and other assorted tips for a good recital experience.