In the next year I would imagine there will be a movement to overturn what the CPB has done.
As others keep explaining, the Chevron deference never allowed agencies to defy the law. It merely allowed them to have the final word on how an ambiguous law that applied to them should be interpreted. For example, if Congress passed a law saying "there shouldn't be poison in the water", the EPA would have the final word on whether a particular pesticide at a particular level constitutes "poison". A company couldn't sue and say "we think this is actually harmless". But the EPA couldn't say "this law authorizes us to hang anyone that puts poison in water" and get away with it through Chevron deference.
If something CBP does is challenged on its constitutionality the court doesn't need to go to Chevron, it will say that the enabling legislation is unconstitutional.
Do you have one source for this? A case where someone tried, or a blog post by a legal expert discussing this?