As of right now, no more than 10% of the cost of a Google Lunar X PRIZE mission may be supplied by government funding. For clarity, though, I should note that teams may conduct an unlimited amount of commercially reasonable sales to the government--those don't count against that cap.
I should also note that the final Google Lunar X PRIZE rules set will be issued to teams in the very near future, and to the public shortly thereafter. Percentages other than 10% have been proposed, though they also follow the same logic that drove that rule (addressed in a previous question-answer couplet). Soon we'll see what the final percentages are.