It's so simple even a democrat could understand it.
Enforce the laws against hiring illegals and stop all public assistance to them. When they can't get a job and they can't get welfare, food stamps, AFDC, medical care, etc., they will self deport. At least in Mexico they would be able to work at something. Penalties for hiring illegals have to be very tough. Huge fines, for first time offenses, and then loss of business license for anything after that. If hospitals and doctors want to treat them there would be no reimbursement by either the government or insurance companies. No more anchor babies, either. Until these measures are taking seriously, which they won't be, then nothing will change.