You suppose to solve any problem by kindly explain to the people in win win situation. That is why they pick you as a leader.
Anyway, if you try to blackmail or take any action that similar to it by resigning from your duty, it is not because of you take care of a small group of disappointed people but it seem like you try to run away from the problem and you actually is a failure!
If all the leaders resigned as the express way just because of this, then who will solve the problem?
At the end, we left nothing.