Given the tremendous backlog of both civil and criminal trials, court administrators are no doubt grappling with the need to comply with the requirements of the Sixth Amendment in light of this pandemic where some defendants are sitting in jail and where some civil plaintiffs are entitled to preferences due to their age and physical infirmities.  The Constitution's Sixth Amendment provides:

In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial. By an impartial jury of the state and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him, to have compulsory process for obtaining witnesses in his favor; and to have the assistance of counsel for his defense.

Several parts of the Sixth Amendment are brought into play by the governor's order which has effectively shut down all of our courts.  This puts the governor's order at odds with the Constitution since, to begin with, defendants in criminal cases are not being afforded speedy and public trials.  This may force some defendants into pleading guilty, accepting plea bargains which they would not otherwise agree to or agreeing to non-jury trials despite their innocence.