Such an executive order would probably lie outside the power of the President. The US Constitution does not give the President power do declare whatever he likes and for it to be law. Executive orders only allow the president to exercise powers congress delegated to him, or allow him to boss around his employees (the federal govt including the military).
Admittedly some presidents have declared all kinds of random things in executive orders, many of which have been followed through - it's a bit of a grey area. However this one is pretty clearly outside his power. It's probably outside Congress' power too as I imagine forcing someone to publish violates the first amendment.
I am not a lawyer. Or an American.
