How Can Congress “Check” the Supreme Court?

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Article III Section 2 of the Constitution reads (in part):

The judicial power shall extend to all cases, in law and equity, arising under this Constitution, the laws of the United States, and treaties made, or which shall be made, under their authority;–to all cases affecting ambassadors, other public ministers and consuls;–to all cases of admiralty and maritime jurisdiction;–to controversies to which the United States shall be a party;–to controversies between two or more states;–between a state and citizens of another state;–between citizens of different states;–between citizens of the same state claiming lands under grants of different states, and between a state, or the citizens thereof, and foreign states, citizens or subjects.

In all cases affecting ambassadors, other public ministers and consuls, and those in which a state shall be party, the Supreme Court shall have original jurisdiction. In all the other cases before mentioned, the Supreme Court shall have appellate jurisdiction, both as to law and fact, with such exceptions, and under such regulations as the Congress shall make.

Since the court has constitutionally mandated jurisdiction only over disputes between states and the like, Congress can use its Article III power to decide what kinds of cases the Supreme Court may hear on appeal, as well as whether lower federal courts exist at all, and thus what cases they are permitted to hear.

Congress can pass legislation to “strip” the court of jurisdiction over constitutional challenges to specific legislation — the Green New Deal, for example, or HR1, the sweeping set of reforms first approved by the Democratic House in 2019 that includes establishing automatic voter registration, making Election Day a national holiday, and ending partisan gerrymandering.  It could also strip the Supreme Court’s jurisdiction over whole areas of law, such as climate legislation.