If President Roosevelt declared that Hawaii was being invaded, the Executive of Hawaii could ... Second, Congress can suspend the Privilege of the Wit of Habeas Corpus "when in Cases of Rebellion ...

They can declare presidential actions unconstitutional. For example, in US v Nixon (1974), the Supreme Court ruled the president does not have executive-privilege immunity from court actions.

Section 1 of EO 464 requires presidential approval of all ... subordinate officials of the government. It declared the doctrine of executive privilege shouldn’t be overextended to cover minor ...

This is why the court declared unconstitutional President Truman’s seizure of steel mills and why it unanimously ruled against Nixon’s claim of a right to invoke executive privilege ...