There is no constitutional provision for executive orders, at least not the way in which they are being used today. The President is vested with the "executive power", which simply means he directs the actions of government as directed by law. He is charged with enforcing the laws, he has no power to modify them. He can not issue executive orders describing how to enforce the laws, he can simply enforce them as written.
"All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives." - U S Constitution, Article 1, Section 1
Before assuming office, the President is required to swear to uphold the Constitution, which includes any and all laws complying with it.
The Presidential Oath of Office: "I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will to the best of my Ability, preserve, protect and defend the Constitution of the United States."U S Constitution, Article 2, Section 1, Clause 8
Article 6, Clause 2 states:
"This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land;"
To re-emphasize, the President has sworn an oath to protect all legislation, passed by Congress, in accordance with the Constitution. He can not enforce only a part of those laws. He can not enforce according to a specific interpretation. If there is a need for clarification, only Congress can do so, and the President has an obligation to ask for direction if that is necessary. If the President has suggestions, the Constitution allows that, but he still must enforce the laws as written until the law is amended.