When the US Supreme Court consisted of civil libertarians such as William Douglas, William Brennan, and Thurgood Marshall, Republicans argued that the Supreme Court was coddling criminals and inventing rights. To prevent legislation from the bench, it was necessary, Republicans said, to elect Republican presidents who would appoint a different court that would respect the Constitution.
Law and Order Conservatives were particularly upset by the Miranda decision. These conservatives were too naive to realize that often police are more interested in "solving" a case than they are in justice. Coerced self-incrimination was an easy way for police to "solve" a crime.
Miranda and other rulings reduced the ability of police and prosecutors to "solve" crimes at the expense of the rights of suspects. What the "liberal court" did was to hold accountable the cases brought by police and prosecutors. The liberals' mistake was they failed to hold the police personally accountable for their misdeeds.
The Republicans did give America a different Supreme Court and also different district and appeal courts. Rulings by Republican judges have stripped the Bill of Rights out of the Constitution and made police unaccountable for murder and robbery. In effect, the Republican jurists have turned the police into a criminal organization that is above the law. John Whitehead lays it out for us here.