I think it is more probable that he will ask Congress to pass, in effect, an enabling act and that Congress will do it.
In effect, we've had a series of enabling acts of limited scope. The ACA is such a complex mess that "the Secretary" is empowered to do make all sorts of arbitrary decisions that normally would require legislation. The EPA makes all manner of outrageous decisions, pushing a couple of unfortunate SJC decisions beyond their bounds. Regulating the pollutant CO2; or ditches that may eventually drain to navigable
Awaters; or their recently withdrawn assertion that they could levy outrageous fines without any due process. And don't get me started about the NLRB...
A general enabling act would be unlikely to pass. But, an enabling act with an immigration scope might get buried inside some complex immigration bill when the House and Senate conference. And then, the monster would emerge.