The vast majority of the immigrants being deported are being forced to leave against their will. Why do you think they should have no say in the matter? Forced deportation is violent and cruel, and results in the separation of families.

If either party actually cared about the people, or budgets, or morality, instead of spending tens of thousands of dollars to remove each person, they would just check them in, have them sign a piece of paper, and grant them legal status.