Instead of quitting with dignity right now, Patterson should just do what he thinks is best for the state. Don't worry about trying to win votes in the next election, the next primary. Internally but silently acknowledge that you will not get reelected, and just do the difficult thing. Cut the budget, oust fraud and cronyism, to hell with the toes that get stepped on.
And if he does, he'll find that his chances of reelection will improve. But he can't do it as a gimmick, a tactic -- it is either sincere, and therefore effective, or fake ... and the voters (and his opponents) will sniff it out in a heartbeat.