Article III Section I of the US Constitution states: "The Judicial Power of the United States shall be vested in one supreme court, and in such inferior Courts as the Congress may from time to time ordain and establish..."
Apparently the Republicans in Congress believe that if Congress creates "inferior federal courts" then it can restrict their jurisdiction.
Congressional testimony - Congress, the Court, and the Constitution :
Instead of such measures that add to their miseries, the Congress should take steps to shield state and local governments from the depredations of the Court. Where the danger comes from judicial interpretation of federal statutes, Congress can (and sometimes does) easily forestall the danger by including language about non-preemption of state laws, or declaratory clauses on the rules by which a statute is to be construed. But the greatest blows to federalism in this century have come from the Supreme Court working quite on its own with no other weapon than what it purports to be the Constitution. To begin to reverse that damage, more imaginative approaches are needed. One scholar, for instance, has recently suggested that the enforcement power given to Congress in section 5 of the Fourteenth Amendment can be turned to good use here, to limit rather than expand the reach of judicial power over the states.(see footnote 148)
The Fourteenth Amendment is certainly the major ''culprit'' if we are concerned about reining in the Court. By ''incorporation'' of the Bill of Rights, and by creating under the doctrine of ''substantive due process'' rights which are contained nowhere in the Constitution at all, the Court has used the Fourteenth Amendment to nationalize some of the most important policy questions that the Constitution properly leaves to the states.
A broad approach to this problem would be for Congress to avail itself of its seldom-used power under Article III to regulate and make exceptions to the appellate jurisdiction-as well as its complete authority over the jurisdiction of the lower federal courts. It would take careful draftsmanship to close all the loopholes to judicial creativity, but Congress ought to take up legislation declaring all questions regarding the application of the Bill of Rights to states and local governments off limits for the federal courts at every level. Where the ''extra-constitutional'' rights currently packed into the due process clause are concerned-such as the ''right of privacy'' at the heart of the abortion decisions-even more care would need to be taken in drafting appropriate jurisdictional legislation. For how does one describe a protean legal fiction with sufficient precision so as to exorcise it from the law of the land? The problem is rather like legislating that the courts shall no longer hear cases concerning dragons only to learn that they are hearing cases concerning unicorns instead. But I am convinced it is worth the effort.
For some, the option of ''jurisdiction-stripping'' by statute poses a potential difficulty, inasmuch as the legislation could itself be subject to judicial review, and the Court could conceivably declare it unconstitutional.(see footnote 149) But the leading precedents suggest otherwise: if Congress cleanly removes certain types of cases from the Court's jurisdiction, the justices will not dare to act on such cases. Only if the Congress attempts to interfere in how the Court decides the cases it does hear, by predetermining their outcome or by fixing the probative value of evidence in a constitutional case, will the justices strike down purported efforts to regulate their jurisdiction-and rightly so.(see footnote 150) Avoid that sort of problem, and this congressional power can be a potent check on the Court.
Not only that, Congress can restrict the appellate jurisdiction of the Suprme Court itself! The Constitution, Art. III, section 2, gives the jursidiction of the Supreme Court.
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 [Modified by Amendment XI]; — 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.