The 25th Amendment outlines the procedure to be followed if the president is incapacitated. The procedure is laid out in stages, and every stage gives the president the benefit of the doubt. A president with a minimal ability to respond can probably defeat any effort to remove him from power. If he has support from a significant minority in even one congressional chamber he certainly can defeat any such effort.
Step #1 in the process enables the vice president and a majority of the Cabinet, “or of such other body as Congress may by law provide” to send Congress a “written declaration that the president is unable to discharge the powers and duties of his office.” If they do so the vice president assumes the president’s duties and becomes acting president.
Congress has never provided for any “other body” to act, so the decision is made by the vice president and the president’s Cabinet. No action is possible unless the vice president agrees. If he does agree, then at least eight members of the 15-person Cabinet must sign on.
Of course, the president selected the vice president as his running mate and the president nominated all Cabinet officers. So people who owe their offices to the president must certify that he cannot function; it is not enough to allege he is erratic, dictatorial, or misguided. And they must present their statement in public. Anonymous hit pieces in the New York Times don’t count.
Could Congress pass a law that defines more carefully what “unable to discharge” means? Yes, but the courts probably wouldn’t recognize it. When the Constitution grants specialized powers to named assemblies (such as when Congress, a state legislature, or a convention acts in the constitutional amendment process), the courts generally hold that statutes can’t regulate their decisions. (The Constitution’s Necessary and Proper Clause doesn’t cover the situation either, because the decision-making group is not “the Government,” a “Department,” or an “Officer.”)
Suppose the vice president and a Cabinet majority nevertheless decide to issue an “unable to discharge” statement. Step #2 gives the president a way to protect himself. He can send to Congress “his written declaration that no inability exists.” Once he does so he automatically re-takes power. Thus, Step # 2 gives the president a way to immediately countermand what the vice president and Cabinet have done. If they wish to persevere, they must immediately proceed to Step #3: They must send to Congress, within four days, another declaration insisting the president cannot discharge the powers and duties of his office.
If the vice president and Cabinet delay more than four days, the process is over and the president has won. Even if they otherwise could act within four days, it will take the president a good deal less than that to fire every Cabinet member who voted against him. In that case, they won’t have the qualifications as “principal officers” needed to vote against him a second time.
Suppose, though, that they anticipate such a response, and in the short interval between the president’s response to Congress and their dismissal, they manage to transmit a second “unable to discharge” message to Congress. This gets us to step #4.
Now Congress decides the issue. However, the decision-making process is, once again, heavily stacked in favor of the president. To remove the president from power, Congress must assemble within 48 hours (if not already in session), and there must be a two thirds vote for removal in each chamber within about three weeks.
This procedure is much tougher than impeachment-and-removal. Impeachment requires only a majority of the House, and there are no constitutional time limits. Under the 25th Amendment, however, if a minority in either single chamber can stall proceedings for about three weeks the president wins.
So Trump-haters who can’t wait till the next election should fix their hopes on impeachment, not on the 25th Amendment. For impeachment, though, you need a proven crime or a real breach of fiduciary duty. Here again, blind hatred and unproved allegations don’t count.