President Hastert would be...something.
A President in office currently under blackmail for pedophiliac acts he'd committed? If it came out (and, really, how could it not come out when the sitting President has to cut gigantic checks to some random guy), it'd be the biggest scandal in American history.
This is actually... very interesting... I'm not thinking about writing a TL where something along these lines happens 
I dare you to do it (though maybe you could "update" it by replacing Hastert with Roy Moore.
Not to mention, Hastert was a lot closer to the presidency in his prime than Moore could ever be in his.
