It's interesting that the latest trend amongst his opponents is to talk about his "fitness" for office.
Well, here's the rub. There is no criteria for "fitness", nor will there be one US federal politician (Congressman or Senator) who will step forward and suggest it, because when they do they are all caught in the same web. As much as they all want to bellow at POTUS, they all know that once they set a criteria they all stand to be measured against it.
Likewise, as silly as it seems, they will never force the President to get a mental health examination. If they did that, and if he passed the test, which he probably would (there is a big difference between being "unfit" and being "outrageous"), he would have clinical proof that he is sane, and none of them - except Trump - want to live with that outcome.
So bellow as much as you want, POTUS is doing what he promised to do - upset the status quo. This is good for everyone. Bright minds will find a way to seize on this.