As each of those go, those on the other end of the spectrum (tax paying, self sufficient, demonstrative effort to integrate into American society by English language and the like) get green cards with no chance of citizenship or, at the very least, a much longer path than they would have had if they'd come legally.
IOW, you make the expulsion of the chaff the key for allowing the wheat to stay. The burden is on the illegals to show how they are a benefit to the country, it isn't on the country to prove otherwise.
This is a compassionate policy, but it has to start with the comprehensive position of deporting all who are here illegally and enforcing the law. Exceptions are introduced only once it is shown that the law is being enforced.
There should be a time limit. Say six months. Any illegal found here after six months will have no chance for citizenship.
Empower state and local law enforcement with incarceration and deportation abilities.
Make everyone re-apply for the varied welfare benefits. Must show up in person and show a birth certificate. Anchor babies get to stay, stupid law, but mom and dad have to go. Baby becomes ward of the state in that case, mom and dad forfeit parental rights.
Occasionally, offer rewards to citizens for leads to illegals. This gets around the inevitable "profiling" and "discrimination" law suits.
How can an illegal pay taxes when it is illegal for him to be employed in this country? That is, if we are really enforcing the law and all. Is Trump going after the cheap labor express that hires illegals? Or is that too harsh?