Answer
The voters do indirectly have power over the Supreme Court, since the justices of the Supreme Court are appointed by the President who is elected by the voters; hence, if the voters have chosen the right kind of President, that President will in turn choose the right kind of Supreme Court justices. If this is not sufficient to check the power of the Supreme Court, an alternative strategy would be to create, by means of a constitutional amendment, a mechanism by which a referendum can be held on any Supreme Court decision, which the voters will then be able to overturn if they so desire. (We could even put ALL Supreme Court decisions to a vote by the general public, atlhough I doubt that this would be necessary.) This process would be somewhat similar to the referendum process on the state level in California, where a court decision legalizing same-sex marriage were subsequently overturned by a referendum.
Answer
Individual citizens don't have recourse for directly checking the power of the Supreme Court, nor should they, in my opinion.
The Court plays an important role in our nation's systems of checks and balances. Without separation of powers and an independent judiciary within a tripartite government, the nation's citizens are at greater risk of tyranny from either or both of the other branches. The Founding Fathers recognized this danger and deliberately fashioned a system of government that, while far from perfect, comes closer to ensuring personal liberty than most other political models.
Of our three branches of government - Executive, Legislative, and Judicial - the judiciary is the weakest. It has no power to create new legislation, nor does it have the means of directly enforcing its mandates. Those are two limitations written into our Constitution that prevent the Supreme Court from wielding too much power.
Likewise, our system of government provides a means for preventing the President and Congress from becoming despotic, passing and enforcing laws that infringe the rights of its citizens. We've seen attempts at this in both the distant and recent past. For example, after emancipation, when states tried to enact laws that violated African-Americans' civil rights, the Supreme Court (eventually) analyzed these laws, determined many were unconstitutional, and provided a rational basis for the President and Legislature to effect changes for the benefit of those oppressed.
On the other hand, as with Congress and the President, there have been times when the Supreme Court has seemed to overstep its authority by exercising judicial activism, applying a broader interpretation to the Constitution than many people believe appropriate, which can have the effect of legislating from the bench. This can, at times, be seen as an abuse of power (usually by the party with opposing interests). Make no mistake - both conservative and liberal majorities have made decisions that appeared unjust to minority interests (by minority, I mean any person who felt a decision was in conflict with their personal or political beliefs).
The opposite of activism is judicial restraint, which means the Court takes a more hands-off approach to judicial review, allowing Congress a broader exercise of its powers. This can work well if Congress is legislating responsibly, and not overstepping its Constitutional authority by infringing the rights of the people.
At times, however, judicial restraint has allowed the government to pass and enforce oppressive laws, so both restraint and activism have some inherent flaws. The ideal is a well-balanced and thoughtful approach that ensures the other branches don't abuse their power, without infringing on the ability of those branches to do their jobs.
While some people believe they should have a greater voice in the decisions of the Supreme Court, it's important to recognize the danger associated with being able to influence a Court charged with upholding the Constitution. The Founding Fathers intended to insulate the judiciary from the pressures and demands of special interest groups; they are not intended to be an extension of the will of the people, but a protection against that will.
This is why members of the Supreme Court are nominated by the sitting President and approved (or disapproved) by the Senate, and also why Justices are afforded lifetime commissions. These practices help protect the Supreme Court from political pressure, the need to please a constituency, and the distraction of the election process, all of which would impact the (admittedly unattainable) goal of impartiality and independent thought.
The best a citizen can hope for is that the Court will render decisions that are as fair as humanly possible, and protect the rights of the public and the government, without creating undue hardship for anyone. It is important to recognize that judgments are made by humans, and that all humans (including Supreme Court justices) subscribe to some type of ideology that informs their opinions. No matter the decision rendered or process used to arrive at that decision, someone, somewhere, will be happy with the result and someone else will be unhappy. Such is an unavoidable consequence of government, in general.
For more information, see Related Questions, below.
Both Congress and the President have the ability to check the power of the Supreme Court, but Congress exerts more influence than the President:
Legislative branch checks on Supreme Court
Executive branch checks on Supreme Court
For more information, see Related Questions, below.
Congress can check the power of the Supreme Court by introducing amendments to the Constitution.
Supreme Court interprets the law according to the constitution so they can stop, repeal, or support a law.
farts daddy
The Supreme Court gained the power to declare laws unconstitutional
In the United States, the Supreme Court is vested with the power to settle disputes. The Supreme Court was established in Article III of the U.S. Constitution.
The President checks the power of the Supreme Court by appointing Supreme Court justices and the Chief Justice (subject to Senate confirmation).
The Supreme Court can check the power of Congress by ruling legislation passed by Congress is unconstitutional. The Supreme Court can do this when they a presented with an opportunity to hear a case which disputes a law. The supreme court's decision is final because it is the highest court in America.
The U.S. Supreme Court has the power to declare an act of Congress unconstitutional.
Congress can check the power of the Supreme Court by introducing amendments to the Constitution.
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People.
The Congress and the Supreme Court provide a constitutional check on the President's powers
the supreme court has the power to interpret the laws no matter what
The Legislative Branch
they can issue a supreme court decision