The President has absolutely no business interpreting the Constitution any way he wants, so he can do anything he likes. Which is exactly what your boy Abe Lincoln did.
Really? I see the part where Congress can maintain an army and a navy, but not separate branches of the military like an air force or a marine corps. Much less a CIA, FAA, etc., etc.
The president and congress can, and do, assume powers under the Constitution that are implied. The Supreme Court may or may not agree with them, see the line-item veto for a recent example.