Yes, the President can bypass the Constitution and Congress with an executive order. There are at least two checks and balances.
1. The Congress can defund an executive order, or pass a law to counter it, or both.
2. A law suit brought to the Supreme Court can give the Court the opportunity to declare the order unconstitutional.
Thanks you for the additional info.
Now, what if a president declares "Martial Law"? Does that, even temporarily, suspend the right of Congress to act? or the Supreme Court?