Mass deportations and the courts
After Arizona passed their immigration law SB1070, several lawsuits were filed that resulted in tying it up in court for about two years.
If as President you decide to pursue mass deportations - even if you think you have the full legal right to do so - the ACLU and other groups aren't going to just let you do what you want. They're going to try to halt your plans in the courts and they might be able to tie up your plans for months or years. Those groups aren't going to be open to a deal.