No one does like being caugh lying.
I find the whole "free speech" angle to this fascinating.
In older times "free speech" meant you are able to express your opinion without fear of beeing punished for it.
However you were also free to bear the consequences of your speech, e.g. others discussing your staments and call you an idiot or liar.
Today, the "free speech" argument is more and more used to supress discussion about statements one has made and to avoid the consequences.
Exposing wrong facts, dissenting opinions, even calling a liar a liar is free speech as well.
So in fact "free speech" in this case is used as argument to effectively limit free speech, not only of the political opponent, but also of neutral observers.
However, the fact that the US conservatives are using this tactic is quite understandable.
There simply is no longer any rational argument they could use to ask voters to vote for their broken agenda or their idiotic candidates.
Since their only tactic left is lying to the general public, suppressing dissent and neutral observers becomes essential...