Congressional inaction isn't assent. The Constitution clearly and explicitly gives the power of the purse to Congress (and this is also the understanding of I think Madison in the Federalist Papers and the interpretation we've had for now almost the entire history of the US so there's no reasonable dispute of this). Until Congress passes a law allowing this the president is constitutionally obligated to take care of the laws passed.

Though you do have a point of even if it's illegal who will enforce it? The courts have started to some but are necessarily reactive and slow.