. . . I simply don't see a way to track down and deport every illegal in the country . . .
Like so many things, absolute perfection can't be achieved, so you're right, we can't track down and deport EVERY illegal. But we CAN deport a LOT of them. Take a look at the numbers for transporting Mexican illegals, overwhelmingly the largest group.
1. Take 1000 buses. Sounds like a lot, but that's how many were ruined in NOLA - one medium sized Southern city - during Katrina.
2. Put 40 illegals on each bus and run them down to the border. That's 40,000 illegals.
3. 3 trips a week per bus. That's 120,000 illegals per week.
4. 100 weeks - less than 2 years - and there's your 12,000,000 illegal Mexicans.
Granted, CATCHING them will be a challenge - especially after the first year or two. (End "catch and release" and move to "catch and deport.") But once you've GOT them, transporting them is a minor issue.
Cost? Say, a million dollars per bus per year. Heck, make it TWO million dollars per bus per year, to pay for drivers, guards, gas, and maintenance. That's a two billion dollar a year program. In Texas alone the cost to educate, medicate, and incarcerate illegal aliens is estimated as being between 4 and 12 billion dollars a year. Yes, the numbers are fuzzy, but we CAN do it, and it makes economic sense to do it.
There's precedent for a major effort in this area - back in the 1950's, Eisenhower's
Operation Wetback deported over 1 million illegals the first year, and a lot of illegals then "self-deported." Unfortunately, with no wall and no real penalties for US employers who hired illegals, the program wasn't as successful as it could have been. We can do better today.