The court has to take into consideration whether a law is considered constitutional or unconstitutional depending on whether a law is upheld by the constitution or not. The constitution has to support a law for it not to be void.
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It allowed the Supreme Court to overrule an unconstitutional law.
Nothing, unless a party with standing to challenge the law files suit against the United States in US District Court, the losing party appeals the case to the appropriate US Court of Appeals Circuit Court (usually), and the subsequent losing party files a petition for a writ of certiorari (request to review the case) with the US Supreme Court. If they grant cert (accept the case), the Supreme Court will evaluate whether the law conforms to the US Constitution either in general, or as applied. If the Court determines the law is unconstitutional, it will be nullified and rendered unenforceable. It is important to note that the US Supreme Court does not systematically review every law Congress passes. Someone who is severely and directly, negatively affected by the law, and has a grievance that can be resolved by a court, must file suit and exhaust the required appeals process before the Supreme Court can review the case (and the law).
The case must be unique and important in order for the Supreme Court to accept the case. The case can also be accepted if it is to resolve a conflict of law.
The Supreme Court amends laws and interprets law.
No the Congress can not nullify a ruling of the Supreme Court. The Congress would have to rewrite the law which the Supreme Court had declared unconstitutional. Then the new law could overrule the Supreme Court IF the new law was declared constitutional if/when appealed.