no it can not be unconstitutional
No. The Supreme Court has the ability to declare something unconstitutional or not. If they have declared something unconstitutional then there is nothing the president can do about it.
Judicial
the president
The federal courts can check the Presidents power by that courts can declare executive actions unconstitutional.
The Executive branch
When was slavery declared unconstitutional in the united States of America?
the line-item veto
Kerala High Court in 1997 declared that bandhs are unconstitutional.
It declared several key programs unconstitutional.
Then you or it is declared Unconstitutional.
Redistricting was not declared unconstitutional in the 1963 case Gray v. Sanders. It was after that.
The Senate must approve the President's appointments, and Congress can override a Presidential veto. Also, the Supreme Court can name a President's actions as unconstitutional.