"If you do what we want we won't force you to" is as old as legislation.

They aren't saying do X or we will pass legislation about Y. They are saying do X or we will pass legislation forcing you to do X. The "widespread voter fraud" story is exactly the kind of extremist rhetoric that they are talking about writing legislation against spreading.

Except that X and Y can't be exactly the same thing when X is content-based censorship of political speech, because then a law requiring X would be unconstitutional. So they threaten a Y which is not quite the same but still nothing they want, in order to make them do X anyway.