I favor enforcing the laws that are on the books. I realize this is a novel approach but, by golly, it just might work.
As far as rounding up 10 million, that's a straw man. You don't have to round them up. You declare that all undocumented workers (p.c. for illegal aliens) have 30 days to leave the country or they will be rounded up, documented by photograph, fingerprint and DNA. Then they can leave they same way they came in....walking across the border. They sneaked across a border into this country somehow, they can damn well sneak back.
As an alternative, how about we, as a nation, adopted a Law of Reciprocity? In other words, we amend all our immigrations laws to make them identical with the immigration law of the origin of the illegal alien, i.e., if you are from Mexico, you will be adjudicated and held to the same laws illegals in Mexico, or Guatemala, or Nicaragua, or wherever. Hey if it's OK for other countries to have and enforce strict immigration policies, there is no reason for the US not to do the same. After all, most of the illegals from the last 30 years, in my opinion, care nothing for assimilating, learn and adopt a new culture, learn English as their primary language but owe their entire loyalty to the country from which they came. Therefore since they love that country so much they should have no problem abiding by that country's immigration laws. It's as plain as the nose on your face.
I like the way you think.