This
methodology of rounding up the "bad folks" goes back to at least
World War II, wherein they rounded up all folks of
Japanese heritage. There are good and bad points to the practice.
It can be easy to just "round 'em up" and start checking the paperwork of folks the government thinks may be involved with non-good things. First off, if they're here on a visa, they should keep their papers in order. If they're here illegally, they should be returned to their country of origin, or they should apply for citizenship or an extension. The problem rests with the US government, and its having the funding to track and follow up on "guests". It seems that the US is only concerned when a major crime has been committed or when it is convenient to track down someone to export them, as is the case with Liberty Shield.
The bad thing is that decent, hard working folks who have gone through the naturalization process and have established a life, a family and a home in the US will get contstantly reminded that they weren't always "OK". It can be disconcerting when they expect the rights they have worked for to be present when needed, only to find out it isn't always the case.
My views on the current knee-jerk reactions by the lawmakers are that there will be a revolt when people start actually paying attention, and begin to notice the erosion of civil liberties. There's a fine balance point between safety versus rights, and it is impossible to please everybody. Unfortunately, rounding them up at the corral is convenient when the government wants to get things done quickly. I doubt it will be the last time you will see the technique used.