Forget the politics for a moment.
How many of us can actually prove that our parents are naturalized citizens? If you've been here for a few generations, I bet you can't find the records. Maybe your parents' parents were illegal. Very likely some relative was. My wife is deep into genealogy, and though we know when some (not all) of the past generations entered the country, I think only one of my grandparents had papers we could find. All the rest are lost to the sands of time. Another grandparent was a native American; did she come into the country illegally, 20,000 years ago? I guess there was no rule, one way of the other.
Sounds like nightmare to me. All for news bites to someone's base, and not for anything that actually matters to the health of the country. Move on to real problems. Social security. A some-what balanced budget instead of printing money and raising the debt ceiling. That, to me, is a conservative value. Tell people some hard truth about money.