What specific constitutional checks are there that restrain the Supreme Court?What specific constitutional checks are there that restrain the Supreme Court?
The major check on the Supreme Court has to do with the fact that the Supreme Court has no power to legislate or to enforce its decisions.
The Supreme Court does make law when it hands down decisions. However, it cannot simply create its own laws. It may only make law in the areas that have been presented to it. For example, the Court could not possibly make a law or laws to settle the issue of what should be done to Medicare and Social Security. This limits the power of the Court.
When the Court makes decisions, it must rely on the executive branch to enforce them. It cannot simply go out and enforce its decisions. An example of this could be seen in the aftermath of Brown v. Board of Education. There was much resistance to this decision and there were times (notably in Little Rock, Arkansas) when the executive branch had to act to enforce the Court's decision. If the Court goes too far, it risks having the executive refuse to enforce its decisions.
Of course, the President appoints justices and the Senate confirms them. This may be seen as a check, but it has no lasting impact once the process is over. The things mentioned above are what really work to restrain the Court from being able to take too much power.
There is also the possibilty of impeachment, but that is essentially never used. Finally, the Congress can place limits on what sorts of cases the Court may hear.
The restrictions on the Supreme Court seem less restrictive than on other branches; but they are indeed there. Justices of the Court are appointed by the President with the advice and consent of the Senate. The importance of this step was quite apparent in the recent appointment of Justice Kagan. The ability to thus restrain the court is "long term," as has been illustrated by how many Justices are on the Court long after the President who appointed them has left office. Congress has the power to increase or lower the number of Justices who sit on the Court; Franklin Roosevelt toyed with the idea of legislation to increase the number of Justices, but abandoned the plan. There have been as few as five on occasion. Also, Congress may determine the Jurisdiction of the Court; but the Court itself may be able to avoid this limitation if it finds that the limitation itself violates some provision of the Constitution. Congress may also propose Constitutional Amendments to overturn Court decisions; although this has not worked thus far.