They should follow the Biden Rule.

While it is true that the president has the Constitutional prerogative to nominate a person to the federal judiciary, there is absolutely no Constitutional mandate that the U.S. Senate must approve or even consider the person(s) so nominated.  It is entirely within the Congressional prerogative to refuse  to consider nominees or any thing else the president proposes.  Congress is after all a separate but equal branch of the federal government and not just a rubber stamp for a dictatorial chief executive.