That is a False Choice Fallacy.
(Also known as False: Dichotomy, Either/Or, Black/White, and probably a few others. Same thing. Only two choices, usually on the extremes, are given, and then argued away.)
Unfortunately in terms of “false choice”, or “false dilemma” - your solution of massive repatriation (voluntary or not) is one extreme, and open border liberals are the other.
I propose a middle way, one which we control.
Realistically a middle way is the best that will happen.
The only question is WHO will structure the middle way and control the terms. Not people who hold to either extreme, though some, not all, of each side’s demands must be met.
Hopefully the process will be controlled by people with a love for American traditions, individual liberty and the long term survival of American values.
This would NOT (MUST NOT) be obama nor the democrat party, given where they have devolved under obama pelosi reid et al.