I know its not the point of your article, but there's some real head-scratchers that make me support this even further. For example, in 2000, we caught 1.6 Million illegal immigrants entering and we basically said: "Well, uh, this is bad, we should do something, maybe a future congress and president will actually stand up and do our job." And we've been saying it every year since. The problem with the number is that it only measures arrested.
Also, if you enter the country illegally, you are a criminal. If i entered India illegally, I'd be considered a criminal. If I entered the UK illegally, I'd be considered a criminal. And both of those countries (while they may not go looking for me) would immediately deport me or jail me if I was made aware to the authorities. So why is it wrong for us to run our country exactly like this.
As for cost, I suspect that (again) we will never have a 2000 mile border wall. But its logical to install walls in places that are known trafficking points or where we don't have reasonable natural barriers to entry.
As for illegals who came here illegally vs. those who overstay a visa. There are two key differences: 1) The person who got a visa is known to the government (they've registered to get the original visa) and 2) most came over with some kind of school or work visa so have a skillset they offer to society.
But its irrelevant. Neither side is changing their positions (well, except for Dems who 10 years ago completely agreed with securing the border but somehow have changed). Some people believe walls work, and some believe they are immoral (unless being used on their own property).