The answer to this question is 100% dependent on the individual player. There is no one size fits all answer. You are trying to convince a player to act a certain way, and that's simply hard.
That being said, what you've described sounds an aweful lot like the bumpers they put on bowling lanes to let kids bowl without getting gutter balls. Many people respond positively when those bumpers are taken away, and they scratch a few frames.
In other words, let the player sign their character's own death warrant. Well, perhaps not that far. You mentioned you don't want them to die. But you can have their actions take the group substantially further from the goal. Perhaps the quest was to convince Noble A to declare war on Noble B. It wasn't a hard task before, especially since your group has the best bard since the invention of salsa! Want to attack the government official? Fine! Quest is the same, only now you have to do it from a dank cell in the bottom of the tower. You have to work through several irreputable individuals who have connections outside of the tower to influence Noble A from within your cell. And, once you do, now you owe someone a favor... and it's not the kind of person that you want to have to owe a favor.
A handful of these typically leads groups to reign in their trouble-member. Actions have consequences. Actions have consequences. In fact, you may find this increases the excitement level of the campaign, simply because players know that their actions do indeed have consequences.
