There are many limits that are placed on the power of the Supreme Court of the United States. This is why Alexander Hamilton said that the judicial branch was the “least dangerous branch” of the national government.
First, the Supreme Court cannot legislate. It cannot make law on just any topic that it would like to. It has to wait until cases are brought before it. This means that there are many areas in which the Supreme Court really cannot have any influence at all. In this sense, it is only a reactive branch and not one that can go out and legislate on its own.
Second, the Supreme Court has no enforcement powers of its own. It can make decisions, but it must rely on the other branches to enforce them. This point is famously made by Andrew Jackson’s (probably apocryphal) line in which he said “the Supreme Court has made its decision (against Indian Removal) now let it enforce it.” The point here is that the Supreme Court cannot make decisions that are too controversial lest they not be enforced.
Finally, the Court can have its jurisdiction changed by Congress. Congress cannot change its original jurisdiction, but it can change its appellate jurisdiction. This means that if the Supreme Court is seen to go too far, it might cause Congress to move to take away some of its jurisdiction.
These limits, and others, make it harder for the Supreme Court to take too much power for itself.