I'm going to use an example that I know of a president who has killed himself, although not in office.
His name is Roh Moo-hyun.
Famed lawyer, fighter for democracy for decades. He became especially famous in the live trials in the 80s, when he tearfully asks ex-president Chun Doo-hwan "don't you care about the people's money" or something like that for Chun's massive embezzlement scheme.
Democracy ensues, political parties coagulate and fall apart. After many years Roh finally gains power in 2003. It seems it is off to a rosy 4 years.
It became a trainwreck. The Sunshine policy was not helpful at all in bringing the two Koreas together, youth unemployment was increasing, and the charisma of Roh broke under pressure of the press. His identity as a eloquent, down-to-earth lawyer became jeered at and he became more like a clown in a suit. There even was a crisis where the opposition launched a half-assed coup and impeached the president for several days. Although this brought the people together to heartily denounce the opposition party, it still was insufficient to make Roh more popular.
The situation became worse after he left the presidency. His subordinates and family became accused of bribery and embezzlement. A few days after returning to his hometown from being questioned by the police, Roh committed suicide by throwing himself off a small cliff.
The reaction was very different between the political parties. The conservatives still jeered at this fact, claiming that he killed himself because he couldn't face his own sins. The liberals showed solidarity in mourning for Roh; many believed he died after the realisation that, on top of all that was happening to him and his family, his vision of Korea would never be realised.
Of course, Roh's death is much less shock than Nixon's hypothetical actions. But the result would still be similar - the opposition would try to frame him as a crazy man who belonged to a madhouse. The leading government would try to show through this incident that the press had broken the President, and that this tragedy is a example of how the press should never go too far.
I know what happened to Roh. I do not mean to cause offense, but this is a far,
far graver situation. Not compatible. There had been a Constitutional crisis for over a year, that was causing America to be torn apart. Things weren't getting done, at all. Watergate was HUGE. And this... good Lord! It would send the far right out of control, and the parties would descend into war, possibly.
America is also not used to this kind of thing. This was the culmination of all the radical social changes of the past ten years-Vietnam, race, everything. Whether it's the indictment of a public figure, the loss of innocence about the Presidency, the sheer amount of "black stuff" Nixon is going to reveal is going to shatter America's psyche further(we are weak when it comes to our image of reality), or just seeing blood on the TV-this will be live, in front of millions of viewers, right before the end. (People were thinking about a trial or a possible coup. Rumors spread wildly about what Nixon might do. Thankfully, none of that happened.)
And as I've mentioned, the international fallout could be so much larger. This was still a Cold War world, in which many foreign leaders supported the dead President over Congress and the justice system. What happens if they think Nixon was taken down by a coup and hounded into public suicide? That's something that worries me even more than the bubbling right wing in the US. Dobrynin's memoirs about what Moscow thought of the whole mess are just arguably the most prominent example-men who had Stalin as their formative political experience just could not accept that a leader, one who had not so long ago won a landslide of epic proportions, could honestly be forced out by the people, damn the damage this does to the international scene or to the USA's interests. They could not understand the mechanics of a constitutional, legal process by a Senate, aided by the Supreme Court. Without blood or tanks or anything. It was a very quick turnaround, don't forget. I don't think their minds were capable of conceiving it-there is to this day no parallel in Russian-or Chinese, or Arab-history. It did not make SENSE for them, the official story. All for what they considered to be a minor breach of conduct, at worst?
For the men in Moscow, there had to be something else cooking. I would not be surprised if they start hounding the US Congress. Can you imagine? Mao is also dying soon, and it's no guarantee that Deng takes over yet-that's arguably the scariest thing. Mao is a REALLY capricious man-if Nixon kills himself publicly, and the right guy (someone like Kissinger) doesn't take over afterwards and says the right things, who knows what he might do with the still infant, fragile Sino-US relations? What if he doesn't make Hua the successor or let Deng back into the fray? The Sino-Soviet split is still a very raw wound.
And even without all that, there was the recent troubles in the Middle East, and a rapidly changing relationship with the region. King Faisal thought that Watergate was a Jewish-Bolshevik plot, and while they were nowhere near as crude as Faisal, I'm sure the Shah, Assad and Sadat didn't really "get it" either. Same with the Turks-this is after the Cyprus invasion. This is coming off the heels of the oil crisis, and with the region in a severe state of flux. If they do not like the looks of what happens in Washington... On the other side, there are the Israelis, who are at that point going through a rather interesting political transition of their own. Who knows what might happen if they decide they can't rely on the US in such a state?
I can even see troubles in South America with the juntas, if they still come to power and they feel that the US is having trouble with internal "leftism".
And even our allies were shocked and dismayed that people were taking Watergate this far. (I think this shows that America is special in some good ways). As one example, in West Germany, Brandt had to resign because his aide was a Stasi spy. They thought Watergate was insignificant compared to that. They didn't GET all the comparisons of Nixon to Hitler. They even admitted that it showed how little we truly understood Hitler, or Nixon, or both.
This is HUGE. We might even get a Kissinger quasi-Presidency, just to make sure the world doesn't fall apart.