How to prevent players from forcing the veto-holder to give up their veto power?

Question

In this game there is a President and the members of the Senate. Most are good, but a few are evil pretending to be good. Each day the majority attempts to figure out who is evil (using clues), takes that player to court (where they may argue in their own defense), and then the entire Senate votes on whether to convict that player (eliminate them from the game) or acquit them.

Only 2 such trials are allowed per day (at night, the evil players murder someone), but only 1 conviction per day.

The President may secretly be good or evil, and differs from the rest only in that he has a veto ability. If someone is taken to court, the President may at any time before the verdict is declared, instantly acquit or convict them.

He may do this only 1 time.

IMPORTANT EDIT: The President must exercise his veto power while voting is in progress, before the decision of the majority has been made public.

The problem is, the other members of the Senate, unwilling to risk the possibility of an evil President overriding the majority decision to convict an evil player at a crucial point later in the game, have developed a meta where the very first time everyone agrees to convict or acquit someone during the first trial of the game, they vocally demand the President to "waste" his veto power in agreement with the majority vote.

If the President refuses they simply take him to court and convict him, eliminating him from the game.

This effectively reduces the President to a normal player.

How can this sort of meta be prevented?

I've tried giving evil players the ability to temporarily disable the President's veto power, in order to give the President a plausible excuse for not using it immediately. This was an unsatisfactory solution because the evil players did not use it enough for the President's excuse "I was disabled by an evil player" to be convincing. Evil players simply did not care whether the President could veto because it's too early for them to tell whether the President is on their side or not.

Answer 1

It seems like you initially had the veto work all the time, but then figured out that this makes the president too powerful, as she can always override the senate. You tried to nerf it to once per game, but as you found out, that's too much of a nerf, because the other players can compel the President to waste it.

You might have to do another redesign of the veto power of the president.

You could do it like the legislative system in the United States does it: The president has a veto she can use as often as she wants, but the Senate can "veto the veto" with a 2/3 majority. That way the presidential veto is still powerful, but not almighty, because the president still needs at least some support for her veto to stay valid.

This of course creates an interesting situation: When 1/3 of the senate are evil, the President is also evil and Team Evil coordinates properly, then they just won the game because the good players no longer have a veto-proof majority to execute players they know to be evil.

This situation could be solved by forbidding the president from using her veto to protect herself. When the good player believe that the game is in this situation, they can execute the president with a simple majority and still have a chance to win.

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Another option could be to completely redesign the role of the president. For example, you could give the President the sole authority to decide which player is taken to court each round. When the players decide to not convict the player proposed by the president, they then immediately get the option to vote on whether or not to kill off the President instead.