Here you go: "To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions".
A reasonable extrapolation of this is "to provide for calling forth the able-bodied citizenry at large to act in defense and preservation of the nation." The Founding Fathers were thinking in terms of active countering attack by human assailants; you'd be hard-pressed to think they'd oppose doing similar, or taking evasive/defensive action, in the face of natural or accidental "assailants" (imminent tsunami, earthquake, nuke disaster, etc.). The point was being able to call on the populace, insofar as they could, to preserve the nation. The focus, in our current issue, is the "calling" part: we now have the technology to tell nigh unto everyone, at once, to ACT NOW as appropriate (be it take up arms against insurrection/invasion, or seek high ground, or hunker down for nuclear explosion, or whatever large-scale imminent disaster). For strict adherence to the wording of the power: this provides means for the President to call out the unorganized militia, which is a strict and sufficient subset of the broad interpretation of the same wording. This system provides implementation of that enumerated power; that it may be used for other reasonable purposes is a natural consequence of a reasonable exercise of the explicit enumerated power.
Using this for political, or other counter- or un-constitutional, purposes would of course be an abuse of power.
So far all I've found is this is a coordination effort, asking/directing broadcasters to implement a standard protocol. Until someone points me to punitive legislation compelling participation and punishing noncompliance, I'm not seeing a problem.
I appreciate your suspicion of this event based on who's doing it. Doesn't mean it's unmitigated evil incarnate.