Arrested for possession of a controlled substance, what can I do?

The governor cannot act until after a conviction and the odds of the governor caring about some misdemeanor are astronomical. Your best bet is to hire a lawyer, plead not guilty and have the lawyer negotiate a favorable result of some sort with the prosecutor. A conviction, even a misdemeanor, can hurt you forever. For that reason, most states have given prosecutors all sorts of authority. For example, your state might have a diversion program by which you do some community service but never get convicted. You could negotiate a plea bargain to be convicted of something less serious, like a parking violation or disorderly conduct or something like that. A criminal lawyer will know what programs are available and what result is possible. The worse thing to do is to simply plead guilty and live with the conviction.