How does Congress check the power of the US Supreme Court?

How Congress Checks the Supreme Court:

• Senate approves federal judges, including Supreme Court justices (Advise and Consent Clause)
• Impeachment power (House)
• Trial of impeachments (Senate)
• Power to initiate constitutional amendments (to undo supreme court decisions)
• Power to set courts inferior to the Supreme Court
• Power to set jurisdiction of courts (they can tell a court that they can not hear a case on a certain topic, which includes changing the appellate jurisdiction of the Supreme Court)
• Power to alter the size of the Supreme Court (if the size is drastically increased the President may select all the new justices and change the sway of power)

More Information

Congress can check the power of the Supreme Court through the process of Constitutional Amendment. While the Supreme Court can rule that a particular law is unconstitutional, it cannot rule that the Constitution itself is unconstitutional. If the Congress (and 3/4 of the state legislatures) approve a constitutional amendment, it becomes the supreme law of the land, and the Supreme Court cannot overrule the Constitution.

Here is a typical example of how the Congress overcomes the rulings of the Supreme Court:

The 18th amendment was passed by Congress and ratified by the states. That made it illegal to manufacture, sell, or transport alcohol. The SC had no choice but to rule in favor of any law that specified penalties for manufacturing, selling, or transport of alcohol. Many people over the years (1919-1933) went to jail for violating those laws, based upon their constitutionality in light of the 18th amendment.

In 1933, the Congress simply repealed the 18th amendment with the 21st amendment, and the states ratified that amendment. The SC since then has had to rule against any blanket law that prohibits the manufacture, sale, or transport of alcohol.

Several times, the SC has struck down laws that prohibit desecration of the American flag. Their rulings are always based upon the 1st amendment which protects individuals' rights to express themselves, even when that expression is offensive to many, even most other citizens.

If Congress were to pass an amendment that prohibited desecration of the American flag, and it were to be ratified by the majority of the states, the SC would likely have to uphold any laws that provided penalties for said desecration.
Amending the Constitution is a difficult and time-consuming process. It was designed to be that way, so that people could not easily alter our form of government on a whim of the moment.