When we speak of a court's jurisdiction, we are asking "what kinds of cases or controversies can the this court accept?" We might also mean what physical area does the court in question cover, a city, county, state, nation, etc. This is a simpler (though not completely simple) question. Generally (but not always) national sovereignty limits the jurisdiction of the federal courts to the territory of the United States.
The more interesting question is "what is the Supreme Court's legal jurisdiction?" In this regard it might be useful to consult the constitution for some instructions. The constitution says:
In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supremeCourt 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.The quote above is taken and interpreted to create two distinct types of jurisdiction:original and appellate. Let's take a look at both types and then the controversy surrounding one of them.
Original jurisdiction refers to the kinds of cases that would originate in the Supreme Court. They would not start in a lower court first. As you can see from the constitution, there are only a couple of conditions mentioned for these type of cases, namely when a state is a party and involving a foreign ambassador or minister. These latter types almost never occur today due to the modern concept of diplomatic immunity. If we were to describe original jurisdiction in case terms in would involve:
Because the Supreme Court is an "awkward" trial court it asked Congress and received permission to start many of the original jurisdiction cases in lower courts which have better procedures for fact finding. The court does on occasion involve itself in fact finding, but does so by appointing a "master", usually an expert working under the courts power to create a fact record for the Court to consider. Because of these difficulties, there are relatively few "original jurisdiction" cases that come before the court, usually a couple of cases a year (out of 5000-7000 requests), sometimes none at all.
Much more important to the Court is its powerful "appellate" jurisdiction. Though this is a complex subject we will boil it down to two statements:
Notice the qualifications on the second condition suggesting that not every case can be appealed to the U.S. Supreme Court, only those that have exhausted their appeals in the state AND contain a substantial "federal" question. Theoretically this limits what the Supreme Court may review, however in practice they (the Supreme Court) can usually find a way or a basis for reviewing a case if they want to. Nevertheless, in this regard. the Supreme Courts has been quite restrained (Bush v. Gore is an exception) in interfering in what are normally regarded as state court business.
Now to the controversy to which all of the above is preface. Does the Constitution allow Congress to LIMIT the kinds of cases it may hear on appeal? Do the words "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 ." literally mean what they say. I believe they do (a minority opinion to be sure). That is, I am convinced that this provision like the impeachment clause (of the President) was meant to assert the supremacy of Congress. In this interpretation (and not many others) I am an unabashed "whig" (look that one up why don't you).
So far this might not seem too controversial. Let's speculate! Suppose the Congress says that the Supreme Court (and other federal courts) CANNOT hear cases on appeal involving "prayers in school". The description would have to be more technical but let's ignore that for now. Many political scientist's argue that these kind of "limitations" of jurisdiction are themselves unconstitutional but, in this regard, they must ignore Ex Parte McCardle OR create an even more special category for war powers and civil disturbance. For an interesting recent case on this subject see INS v. St Cyr
U.S. history is a long story of tension between the branches of government. In war, the President is clearly ascendant, in the early period Congress was. Today the Supreme Court as assumed an almost "supervisory" role over the other branches. I find this extremely disquieting for the future of "republican" government. It takes a very powerful or popular President such as Jefferson, Jackson, Lincoln or FDR to confront the court and even then they don't always win. We have had a long series of historically "weak" presidents. Maybe that's not bad for the republic either.