There is a checks and balance system for a reason. A President cannot go against the Supreme Court's decisions, if not simply because the Supreme Court decides what is Constitutional and what is not. As a President, they cannot go against that. Every President, from George Washington to Barrack Obama, took an oath to uphold the Constitution. A President can be impeached for acting against the Constitution.
In reality, both the President and Congress sometimes delay acting or fail to fully enforce a Supreme Court decision. This was most notable during the Civil Rights Movement with regard to desegregation, especially before Congress passed the Civil Rights Acts of 1964 and 1968.
Supreme court
Chief Justice of the Supreme Court
President Andrew Jackson is often cited as a president who disobeyed a Supreme Court decision. In 1832, the Court ruled in Worcester v. Georgia that the state could not impose its laws on Native American lands. Jackson reportedly responded by refusing to enforce the ruling, famously stating, "John Marshall has made his decision; now let him enforce it," highlighting the tensions between federal authority and state actions during his presidency.
Chief Justice of the Supreme Court.
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William Howard Taft is the only person to serve as president and one the Supreme Court.
Jimmy Carter
Jackson refused to obey the court's ruling
He took matters into his own hands
supreme court