In the mid-80s, it looked like Ronald Reagan was a goner. He was involved in a huge scandal called Iran-Contra. But he was too popular and he also was able to do some effective crisis control when he essentially did a national address and apologized for what happened.
While it doesn’t seem likely that Donald Trump would do such a thing, he did pretty much apologize after the Access Hollywood tape and so if he really wants to be president all that bad he might do it. He could announce that he’s pardoning all the key figures, apologize and ask that the nation move on.
But Trump is no normal president and it’s very possible he may prefer to start a war with North Korea than risk losing power. Only time will tell, I guess.