The exact source of the term "National Security Emergency" is probably impossible to definitively resolve. Here is my best shot. There was a suggestion of the term in the creation of the EMERGENCY PREPAREDNESS MOBILIZATION BOARD created by Presidential Memorandum under President Ronald Reagan. This multi-agency board was designed to analyze the efforts of the civil agencies to mobilize for national needs in various crisis situations. The effort was forshadowed by a classified and unclassified study by FEMA mandated by President Carter and his national security advisor to determine impacts of a large-scale natural disaster-specifically a S. CALIFORNIA earthquake on the National Security of the US. This had been kicked off when the President and his NSC advisor were flying over Mt. St. Helens in May 1980 and both started speculating on the national security impacts of such a large scale event. While I know longer possess the unclassified version I believe it was numbered FEMA M&A 10.
At any rate, the REAGAN memo was followed by issuance of NSD-47 in 1982 the text of which has been made previously available on this blog and elsewhere.
Then in 1984, the issuance of E.O. 12472 for the first time gave that level of authority to the NCS [National Communications System] which had been operating since the Kennedy Administration under the authority of a Presidential memorandum. Thus, the term "National Security Emergency" was now in official use and although undefined had made its debut in an Executive Order.
In the long struggle to issue a revision to E.O. 10490 (1969) giving the assignments for the civil agencies in the world of civil response and crisis management, E.O. 12656 was issued in November 1988, just after the election of George H.W. Bush. That order while technically amended twice, once for no real reason since the amendment repeated something already in the order, it still exists. When issued it purported to define the term "National Security Emergency" but did so in a largely elliptical fashion rendering it meaningless.
That E.O.  by its own terms is an adminstrative EO and does not actually convey any operational authority. Nor were the assignments made by it every properly funded. Yet, it does again utilize the mysterious term "National Secuiryt Emergency" which appears no where in the US Code and therefore in theory escapes the procedures of the National Emergencies Act of 1976 and other attempts by Congress to delimit Executive Branch emergency authority. There were once over 400 statutes that had "National Emergency" triggers and that number has now declined to about 100. Few of these statutes really vest much additional authority in the President that would justify declaration of a "National Emergency" and since much of the modern Presidency is devoted to making sure that no one really understands what it is doing (especially Congress) in the crisis management and national security realm [probably so that the national security priesthood and its military component can continue to erode Constitutional government] that effort by Congress has largely failed.
Still at the end I believe a comprehensive update of E.O. 12656, now 23 years old would be a good thing.