I think that is a total reasonable response. We want people to knock, and ask to come in. We decide who does and does not.
However, the analogy of the person in your bedroom already doesn't fit. We are talking about families that have been here for 30 years. Our communities do not benefit by ripping the patriarch out of a 3 child household. This is easily verifyable. I find most people sort of agree on the following.....and it really seems like enough.
1) Increase border security permanently, leveraging our technology......but not building a wall costing 40B.
2) Deport criminals with the full cooperation of all agencies. Period. Have an agreement with Mexico to extradite and imprison THERE, not here. We can even contribute to that initiative (and still save money as opposed to incarcerating ourselves)
3) Give the DACA kids a path to citizenship that isn't burdened with red tape and fees. Get them in the system, and have a line for their parents already here. Do this for the sake of stabilizing the communities and families.
4) Adjust how our visa system works. Refugee? Lets be a society of compassion....but smart about it. Want to visit family? Need a return ticket, and a way to properly track you. (this is how most immigrants illegally migrate here.....NOT the southern border) Want permanent residency or citizenship because of a job? Lets do it.
5) Streamline a guest worker program, not letting people be abused, and giving wages that can be meaningful back home. No "slavery" like what happened in Florida with people being beaten, unpaid, and treated sub-human.
6) Reach out to our southern neighbor on common ground, and have Mexico be our ALLY again, rather than denigrate them, and make them defensive.
I mean......is it that hard? Don't people on all sides already agree in principle on these things? Why can we not do it?