[kenj0418]

Congress could definately make this law, but they also delegate many policy details to the executive branch - so this is likely something that could be done by either branch right now.

Regarding the 'petitions'. The 'petitions' in question here have no legal standing at all. It is essentially a way for the current administration to let the people involved feel like their views are being heard. The end result of each of these is generally either a) a canned response about how they can't comment on the petition for whatever reason or b) a rehash of current policy.

The only real impact, if any, of the petition is if they sway the administration by demonstrating what public opinion on the matter is.