You forgot: killing any/all welfare.
My biggest ?: What is wrong with ENFORCING THE CURRENT LAW(S)?
Not a dang thing. That's how Cruz proposes to get rid of the current illegals, including not letting them get welfare. He said it again last night. Enforce the laws on the books: don't let new illegals in, take away their ability to work at otherwise legal jobs, take away their ability to illegally get freebies, deport those who run into the law on their own (which would include those doing illegal jobs, like drug dealing). Dang few could afford to stay here without one or more of the above unblocked. So you don't need PR nightmare secret police raids to round them up. End 'catch and release' by the cops for the worst and the rest will leave on their own just as they arrived on their own.
Better than Trump spending a fortune on bad PR to round them up, give them a vacation to their foreign families, where they fill out the paperwork to come back legalized. I'm sure Jeb's friends will expedite that paperwork. Spend a fortune to have a country full of sanitized 'legals' and a big wall anyone can get papers to cross. The GOPe was slow, but finally figured Trump out. That's why they're pushing Trump over Cruz. Don't enforce current law and really solve the problem; make new law to create a big, visible, process to make the problem legal.