Answer to your question:
Prior to the open border mess being created, I would say: Increase immigration greatly by streamlining the legal process...clear the backlog, and make it easier for more to line up...make sure they embrace our culture like the Hispanics do. While doing that, cut off all social welfare programs for immigrants. Only allow private charity to help them. Private charities will step up. Let 'em in; let 'em work to make America great. Go to the model for immigration which made America great before.
But, that is apparently not an option. Apparently I must choose between open borders and full government aid, or "mass deportation." OK, then I guess the latter, since we can't afford the former. But, I think that is not a fair choice, since there are many options between the extremes. I would halt the active importation of illegals while leaving those who legally apply on 15 year waiting lists. At a minimum, we can start deporting any illegal arrested. I wouldn't call that "mass deportation," but the Left likely would. Would you?