"According to Suetonius in the Lives of the Twelve Caesars (121 AD), [Mad Emperor] Caligula planned to make Incitatus a consul [effectively half-president]." --quoted from Wikipedia. Trump is totally pulling from the lowlights of the Lives of the Caesars. ICE is basically a proscription, in the mode of the tyrant Sulla and later the Emperor Domitian. (Trump is really hitting hard on the Caligula/Nero/Domitian axis).
The historian Tacitus' description of Domitian is pretty Trumpian too: he talks of the Senators fearing the expression on the Emperor's big red face.