As to the jurisdiction of the federal courts, they should have the authority to overrule state laws contravening the Constitution. They should have the power to enforce uniformity in the interpretation of national laws. They should have jurisdiction in all cases involving citizens of other nations.
And most important in assuring domestic order and tranquillity, federal courts should have jurisdiction in conflicts between the states, such as on boundary disputes. They should have jurisdiction in determining causes between one state and the citizens of another, and between the citizens of different states. Only federal courts could impartially judge such cases. The national judiciary should also have jurisdiction in maritime cases, for the latter often involved the rights of foreigners, rights assured to them by treaties which were per se part of the supreme law of the land.
This essay on why the United States Supreme Court should have the authority to overrule state laws which in its judgment contravened the Constitution, and to enforce uniformity in the interpretation of national laws, is self-explanatory. Was there to be a national law, or not? If so desired, there was only one way to accomplish this.