There can only be so many outcomes to the situation. Without a strong political will, and there is none in the Republic at this point, the bad apples of the Ministry won't be thrown out. They'll keep their money, their power, and their discretion.
I don't think this is a fight to the death between Gaymard and his Ministry. I may be overly optimistic but I think the scandal is too frivolous to cause Gaymard to resign, and whoever at the Ministry is leading the mutiny knows it. The government already gave up more than it should have, since Gaymard and his family have been made to move out from their old apartment into a smaller one.
What is most likely is that the campaign is only a warning shot, designed to scare the hell out of Gaymard to get him to go back on his bold actions and restore the precious status quo. Unless he has the courage to resign rather than accept defeat. But in that case, his departure will be in disgrace to the eyes of the world, and only a few will know the real reasons behind it.