A Slip of the Tongue
במדבר כב ,ו: יִ ל־הָרָא אָ נ־הָכְל הָ תַעְו
Baal HaTurim comments that "L'choh oroh li", which means 'Go and curse on my behalf', also has the connotation of 'Go and curse me'.
Little did Balak realize that is precisely what would happen. By the time Bilaam had finished, he had blessed Yisrael and cursed Mo'av. Later, as a result of that curse, it would seem, Balak's daughter would be killed and so would he.
Later, Baal HaTurim comments that when Balak hears Bil'am's prediction that "Those who bless you (Yisrael) are themselves blessed, and those who curse you are themselves cursed", Balak had heard enough. Effectively, Bilaam was announcing that his mission (which had not fared too well until now, as far as Balak was concerned), was doomed to failure, since any curse that he might succeed in pronouncing ('behind G-d's back') would only boomerang on himself. That explains why Balak's patience snapped and, with the rather demeaning command "And now, run away to your place", he declared his mission closed.
