Yes, recorded votes will show who is the liar. But I doubt it will blow up in his face with his flock.
Oh hell no, that would be a plus for him with his flock.
Not with his most devoted flock, but that flock can't get him elected by themselves.
I think undecideds who make up the majority, particularly away from the coasts, are turning away from him in droves because of this kind of thing.
God willing, he will lose this election by the landslide he so richly deserves.