To be fair, the thing that is most oft intended by the idiom is "look, if the cherished first amendment can be restricted, then so too can the second amendment".
It isn't a law, and where I say "might" in my follow-up, it should not be confused with "is" or "will". There are no laws that forbid you from exclaiming fire in a theater. People think there are because Oliver Wendell Holmes made a clumsy aside while explaining a bad decision that has since been overturned.
Either way, the real point to this is that a punishment for negligent use of one's rights (e.g., falsely shouting fire in a crowded theater for the purposes of causing harm to others) is still not remotely the same as banning free exercise of that right, or converting that right into a privilege through licensure, as is being suggested as rational compromises for the second amendment, predicated on a clumsy and wrong-headed interpretation on the first.
We might all prefer it if you had to obtain a license to speak in a theater, on the grounds that yelling fire in one might prove too dangerous a responsibility for average citizens, but I think most of us would agree that it would violate the first amendment quite heinously. The only way to imagine that equivalent restrictions are less heinous when applied to the second amendment is if one takes the second amendment less seriously as a "real" right, or to imagine that such restrictions are common on the first amendment. It isn't less real a right, and such restrictions are not common on the first, despite misuse of the aforementioned idiom.