The US Constitution takes precedence over state constitutions when there are conflicts between amendments, per the Sixth Amendment Supremacy Clause.
The US Supreme Court can't nullify a state constitutional amendment unless it has an opportunity to grant certiorari to a case challenging the state constitution, however. Case law relevant to conflicts between state and federal constitutional conflicts would invariably support the federal constitution. If the State constitutional amendment isn't ruled unconstitutional by the State supreme court, the US Supreme Court would overturn the amendment (if it truly represents a constitutional conflict).
In one recent example, New Jersey voters ratified an amendment to their state constitution allowing them the prerogative to recall Congressmen with whom they were dissatisfied. The New Jersey amendment is unconstitutional under the US Constitution, but the Supreme Court can't do anything about it until voters attempt to recall a Senator or Representative and someone with standing (the Senator or Representative himself) files suit contesting the action.
The case would have to go through the New Jersey court system and the NJ Supreme Court decision appealed to the US Supreme Court before the federal court could make a determination. The process could take several years, or the amendment could remain part of the NJ constitution indefinitely, if it's never acted upon.
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The [State] Supreme Court (or its equivalent) has final authority unless the question being addressed in the state constitution conflicts with the US Constitution, in which case the US Supreme Court has final authority.
It is true that the framers had quite a few conflicts and made some compromises while writing the Constitution. One of the major compromises resulted in the Bill of Rights.
The Supreme Court has jurisdiction over cases involving questions of federal or constitutional law or US treaties.They don't have jurisdiction over matters involving state or municipal laws or state constitutions, unless the case involves a conflict between two states, or a law or ordinance repugnant to the US Constitution.They don't have jurisdiction over cases from state courts if the federal question (constitutional issue or matter of federal law) was not raised at trial and preserved through the appellate process.They don't have jurisdiction cases involving political questions, such as appeals of impeachment.They don't have jurisdiction over cases prohibited by the Constitution or by constitutional Amendment, such as conflicts between the citizens of one state and the government of another (per the 11th Amendment), unless the state(s) waive their 11th Amendment protection or a state official is sued by name.They don't have jurisdiction over cases on matters from which Congress has stripped their appellate jurisdiction, assigning it to another court.
constitution