It is a truism of administrative law that an agency must give reasons for a regulation at the time it is promulgated. Whether or not they are the agency's real reasons, they must be good reasons; among other things the reasons must fit the enabling statute's requirements, and comport with the facts reasonably relied on by the agency.
Moreover, if the agency's regulation is challenged in court, it is (in the main) not open to the agency (or its lawyers from Main Justice) to come up with a new and better set of reasons in a reply brief. The court (with a still quite small list of exceptions) will dismiss justifications that make their first appearance in a brief as “post-hoc rationalizations”. Admittedly, the penalty may not be that steep if the court remands the matter to the agency, which is then free to substitute the new, better reasons for the old, inadequate ones. But agencies dislike remands — they are embarrassing, they consume resources as the docket must be restarted, and they frequently reset the clock, thus requiring the agency either to enter the retroactivity thicket or only make the revised regulation effective from the date of re-promulgation. (This last reason is why clients can be quite happy with a remand, even if it is clear they will eventually lose. There's a lot of money being made in the interim.)
All that is hornbook law. Important. Contested a bit 'round the edges perhaps. But pretty settled otherwise.
But what if the regulation at issue isn't an APA rule but rather an Executive Order pursuant to a power delegated directly to the President in a statute? The ban on post-hoc rationalizations traces to Justice Marshall's brilliant opinion in Overton Park which roots the requirement firmly in the APA.
Besides Overton Park, the other great modern case where the Supreme Court articulates an agency's duty to give reasons, and the Court's unwillingness to consider different reasons, is SEC v. Chenery Corp. The case arose just before the APA was promulgated, so the decision technically wasn't an interpretation of the APA but rather of general principles of administrative law that were codified in the APA; the tradition is to read SEC v. Chenery as both consistent with and explicative of the APA. The decision seems based on fundamental principles of administrative agency review, a system informed by Due Process (and by the non-delegation doctrine), but not directly rooted in it any more than Overton Park.
The source of the rule on post-hoc rationalizations matters because the APA doesn't apply to the President; the APA applies to agencies, and the President is not, the Supreme Court has told us in an application of the Ashwander avoidance canon, an agency for APA purposes. Therefore, if Congress wishes to find out whether it can cram the APA down the President's throat, it will have to do so more explicitly than it has done in the definitions section of § 551. So far Congress has yet to accept that invitation.
Thus the question becomes whether something in the Due Process Clause (or something in the act relied on to issue the Executive Order), can be interpreted to impose an Overton Park-like requirement on the Presidency when the President issues an executive order pursuant to statute.
I suspect that the answer may be No, at least as far as the Due Process clause is concerned. If the President issues a conclusory EO explictly referencing the statute on which he relies, he may have no obligation to give reasons until his action is challenged in court unless the statute empowering him imposes that obligation (and I suspect that they don't, although it would be good if they had hooks that would allow courts to say they do). Once in court, some explanation tying Executive Order's action to the statute's purposes and empowerments is clearly due under any notion of Due Process. In the APA regime, though, that could be the dreaded “post hoc rationalization” — or a straight up violation of Overton Park — since nothing came sooner. But as we know, the APA gives you much more than Due Process does, especially since — courts preferring to do statutory analysis rather than Constitutional exegesis (Ashwander again) — the APA's existence often forestalled the extension of the Due Process revolution to matters covered by the APA regime.
(All this is sparked by a discussion with a colleague about a cursory EO issued pursuant to a statute he is writing about. If anyone knows of an article on the subject, please share.)
[Revised from the original version.]