Holding dirty secrets over the heads of rivals is allegedly an old trick; J Edgar Hoover was said to have a file on everyone. The thing is, the general use of this is selective blackmail--one is having problems with someone in particular and either dumps the dirt on them--almost always this has to be done with plausible deniability because even if one has standing to openly disclose something important about a rival, it looks fishy even if it is quite kosher coming from a rival--in the hope of crippling or destroying them, or one surreptitiously signals or contacts the rival and lets it be known that they can spill these beans and offer terms for not doing it--aka blackmail, in fact I think there might be no legal distinction at all between criminal extortion blackmail where money is what the crooks are after versus blackmail where it is certain actions that are desired. Well, gosh, I suppose there must be a distinction--the politicians who specialize in this sort of game are the one who write statue law after all!
But this is a different case. This is one politician backed up against the wall regarding a whole horde of rivals.
The blackmail trick works against a background that presumes that the general run of politician is reasonably clean. If everyone becomes cynical and is convinced, as Nixon apparently was, that "they all do it" and no one gets ahead without some dirty tricks and backstabbing and secret deals they'd rather keep secret, then politics becomes a game of "OK, he's a crook, but he's my crook!" The nuclear option is not selective. It might start that way. He might use his Federal authority to selectively attack only those he sees as his foes, and assure his friends he has their backs; the FBI will arrest Democrats (and not all Democrats; there were Nixon Democrats after all) and maverick Republicans but leave loyalists alone. But doing it on that massive scale is like selectively nuking some cities in Russia...use it or lose it; once the gloves are off his enemies have nothing to lose and something to gain by dumping the dirty secrets they've been holding against their rivals. They retaliate.
It gets messy to be partisan about these things, then or now. It's a fact for instance that in the 1964 election cycle Barry Goldwater held off from using the knowledge that a certain person connected with the Democrats was gay, holding that there were degrees of dishonor he would not sink to, while I'm pretty sure people like Lyndon Johnson would not be deterred from a like attack on Republicans. Nixon had some reason to believe "everybody does it" although there were certain things he believed that in specific were quite impossible at the time--he believed that President Johnson had his 1968 campaign airplane bugged for instance, but that was technically impossible to do at the time. (I gather that J Edgar Hoover and others who knew better encouraged him to believe it anyway, for their own reasons). Nixon may honestly have believed that everything he did that was ballyhooed as outrageous, such as the Watergate burglary (which was an attempt to steal psychiatric records in the hope they could be used against Democrats in the '72 election cycle) or his orders to the IRS to harass people he regarded as enemies, indeed his keeping and discussing with staff of an Enemies List...that any other politician of Presidential caliber, Democrat or Republican, would and did do the same things. If this were the absolute truth--then even so, rather than selectively mowing down his enemies in one massive operation, all he would accomplish would be to level the field destructively. When the dust settled, the public would have low confidence in any politician, pro or anti Nixon. Insofar as his cynical views were already shared by large sectors of the public anyway, the whole mutual exchange of dirty secrets would just be a tactical situation for them.
But I think actually there are other layers to American politics. Some people go in because they can profit, or because they regard the game of getting and holding power as the course of honor in a competition to rise in status. Others go in because they have causes, because there are issues they care about they want to see through. If someone is going to stay in politics for the career lengths necessary to wind up in offices like Senator or President, they probably have to mix it up a bit; a handful of issues won't sustain a career. But a bunch of issues that the politician sees as ideologically connected can indeed be the basis of a career, particularly that of a crusader against what they see as persistent injustice. Conventional wisdom says that to survive in politics you have to make dirty deals, betray your own cause at least somewhat today, in the hope of fixing what you let slide tomorrow perhaps. But I suspect that it is often true that the crusader type of politician, especially the crusader for the poor against the rich, is careful not to get entangled in truly dirty deals, and is candid with their supporters about the compromises they must make openly. They know that in tilting against establishment windmills they make a lot of powerful enemies, and they can't afford to leave themselves open to cheap shots and easy attacks. A career politician might expose themselves to serious legal liability, knowing that the figures who enforce the laws have their backs. One the police and FBI hate will go down in a hot instant the second they step out of line. Therefore, if they ever do step out of line in terms of the current legal and political environment, it will be in defense of what they think is a noble cause. That way if they are called on it they can use it as a line of attack against injustice and hypocrisy.
So, as a general rule, a Democratic or Republican Congressman or Senator picked at random might have a rap sheet of dirty deals with equal likelihood. A Nixonian selective attack on some of them would be attacking on grounds of dubious business deals, or outrageous conflicts of interest--money would generally be involved, or trading political patronage for support in a dubious matter. However, mixed up in all this would be other attacks--that such and such politician himself is gay, or someone they value on their staff is, or so and so had ties with far left wing parties once upon a time, or a female staffer or a male politician's wife had an abortion.
At this point, the crusader types start bouncing back or standing untouched with higher and higher frequency, as the attacks and counterattacks shatter the facades generally. Someone who is elected in a progressive district and has been open about their support for tolerance of homosexuals or their stand for abortion rights can raise their eyebrows and say, why yes, of course Cynthia had an abortion, or Daryl is gay...so what? They might lose some support, but they might also gain more than they lose. If this office is not entangled in dirty money deals--maybe Nixon's people make one up and frame them, reasoning that with so many dirty money deals going around no one will doubt that these guys do it too. But if they in fact did not do it, the case might fall apart in court, or before getting to court--and then the credibility of those who accused them comes into question.
The upshot might be, after the next couple elections, a House and Senate full of Ralph Nader and Jimmy Carter types--naive true believers hardened by adversity to adopt a strategy of being clean, and their sincerity shines through enough that people believe them.
More likely there are enough cynical voters out there who shrug and say hell, I'm voting for my crook anyway even though he is a crook because everyone knows they are all crooks, so might as well have the crook who says things I like in there. The government is probably safe from being run by the sincere and open I suppose. But those people will still have an extra mantle of credibility the majority of fixers and wheeler-dealers will have to court and marshal in their own causes. And a Congress like that is a death sentence for the Nixon Presidency; a Senate like that might even vote to convict.
I think Nixon understood all this very well. Blackmail is a tactical weapon, not a WMD, because if used as the latter it will surely destroy yourself as well as your foes, and indeed they might come out of it more credibly than you do.