I think we should take the most able-bodied and willing-to-work types among them, give them all full authorization to live here and work in the jobs that the young Americans will no longer take (and thus restaurants closing up their stores). Until all those jobs are FULL. Once they've shown up every day to work for 6 months, give them citizenship.
Then, take all the young Americans who weren't willing to work and send them to Rwanda, or really anywhere close. Get rid of at least several million Americans, I'd much rather have work and family oriented Mexicans in their place - but only to a numerical 'point' where it makes sense. Remove their authorization to come back for a decade.
After that, return to sender all the remaining immigrants who have been here less than 3 years, unless they have a legitimate asylum claim (and asylum must, obviously, be defined in such a way that it can't possibly apply to more than 10% of all immigrants).