Why "round them up"? Make them go home on their own. And here is how you do it. Companies get to write off wages as a buisness expense. So force companies to actually verify the information that they are required to collect. If the information doesn't match, the name and number in the Social Security Administration data base, you can't hire the person, and any wages you pay them can't be used as a deduction when filing taxed. Also the states have to stop providing services to those who can't verify they are here legally. ALL SERVICES, except true emercency medical care. If you go to ER because you have the flu, you are responcible for it. If you go because you just crushed your hand, that is an emercency.
Trust me, in a year or two, they will all be back in thier home land or moved on to another country. I don't just mean "Mexican's". There are illegals here from many, many different countries, so I am not picking on anyone group of people.
And the best thing about doing it this way, is it doesn't cost taxpayers much.