Texas tried it once and failed miserably.
The Supreme Court ruled in Texas vs. White in 1869 that no state could lawfully secede. Their conclusion is based on Article VII of the Constitution, which says that the Union is irreversible. Despite several challenges over the previous 150 years, the Court has remained steadfast in its position. When Texas entered the Union, it became a permanent member of the Constitutional Compact.
The fact that Texas was admitted to the union as an independent country without ever having been a territory gives it the power to secede from the United States. Texas has a significantly better legal position than any other state because of how it entered the Union. This posed some unique challenges for Texas, but it didn’t change the fact that the constitution does not allow for a state’s withdrawal from the union. A constitutional amendment establishing a succession mechanism would have to be adopted for a state to succeed, which is unlikely to happen.
To be honest, I’m not sure what the movement is all about. States are more like their own nations in reality because they are, although within the framework of a federal republic, namely the United States Constitution. As a result, each state has its own constitution, governor, senate, legislature, and judicial system.