I would like to add my two cents into this. The courts seem to have some authority but only in sentencing people. They decide how long each of us stays in prison but when there is a dispute between states or the federal government then its more of an arbitration because a state can't force another state to comply with a decision of the court. There is no enforcement mechanism other than an invasion of that state.
In order to make a state comply with a court decision the congress must enact legistlation raising an army and making them comply. It then becomes an act of congress that enforces the decision of the courts.