Donald Trump and The 25th Amendment

Any attempt to remove Donald Trump from the presidency using the 25th Amendment is likely to fail

Impeachment is actually more likely to work, as I will shortly point out.

The 25th Amendment was written into the US constitution as a way to determine who runs the government if the president is incapacitated. This would mean that the president is so badly injured or so badly ill that he is incapable of functioning in his position. The president's cabinet, or a committee set up by congress, would then send an official letter to congress informing them of the president's incapacity. The Vice President would then be appointed into the executive role until such time as the president recovers. Once he has recovered, he would then begin working as president while the Vice President returns to his position.

Section 4 of the 25th Amendment, however, cover the possibility of a president potentially going mad or being incompetent. While these terms are not used in the amendment, it is clear that its writers assumed that a time might come when the president is unwilling to give up his role, temporary or otherwise, in the face of a 25th Amendment removal.

When this occurs you then have an impasse. If the cabinet remains committed to remove the president but the president remains committed to staying there, then the decision is referred to congress.

And in order for congress to remove the president, a two-thirds majority in both houses is needed to succeed. This is why impeachment is easier (it needs a majority in the house and two-thirds in the senate).

So if Trump's cabinet does theoretically decide that the president should be removed, the following would occur.

1. The Cabinet would write an official letter to congress stating that it is in their considered view that the president is incapable of functioning in his role. As a result, they are appointing the Vice President, Mike Pence, into the president's position. 
2.  Once this has been done, Trump would then write a letter to congress. In this letter he would say that he is fine, is the most intelligent person on the planet, and quite capable of functioning as president. Once this has been done, he would then go back to being president, and Mike Pence would return to being the VP. 
3.  After this, the cabinet would send another letter to congress, saying that Trump is not capable of functioning as president. Once this has been done, the power to make a decision is given to congress. 
4.  Congress now has to decide whether to remove the president. Two-thirds of both houses of congress are required to make this occur. As this is going on, Trump supporters are protesting outside congress, warning the Republicans in congress to not remove the president or there will be hell to pay. Some Republicans vote to remove him, but the magic two-thirds line is not reached because there are enough Trump supporters in congress to prevent the removal. 
5.  Trump remains president and fires his cabinet. Mike Pence resigns. Trump appoints Jared Kushner as VP.

The only way for Trump to be removed from office using the 25th Amendment is if congress makes that decision. And that decision is harder to make than a decision to impeach.