The POTUS is a public servant, not a caudillo.
The Constitution gives him the authority to make SC picks, not some howling mob.
There are a great many conservatives who, silently, are hoping he doesn't knuckle under to the unappeaseables.
The Executive is NOT elected by the "public" and is not subject to the whims of the "public" as per intent of the Founders. He is essentially a monarch for four years above public opinion also as per intent of the Founders.
Nominating Justices is NOT an exercise in democracy as per intent of the Founders. And the lunatic fringe of the lunatic fringe has NO say in this matter.