Here's the fly in the ointment on this issue.
Let's say someone gets arrested for assault who is found to be an illegal immigrant. Do you deport them immediately or do you wait till after trial to prove they are guilty? Remember, in this country, you are innocent to proven guilty. Now, if you choose to wait till after trial, do you allow for them to be let out on bail like any other accused person in a similar type situation? If you say no, where are we going to house them? If you say yes, then, you are allowing an accused violent illegal immigrant back out on the streets.
How are you going to prove to these people that they can trust what we say? We already have screwed over people who came out of the shadows as DACA what Trump has done. Do you think those people are going to trust the US government again?
IF we put something like this in place, the process needs to be done in less than 2 years. Here's why. Let's say we have a President and congress in place that supports this. That doesn't mean in 2 years we will. So, these people will need to be able to come out of the shadows and become citizens in the amount of time it would take for the people in government to change their minds.