We can't find Bin Laden. How are we going to find 12 million people who aren't trying to do anything more than live just like the rest of us?
There are murderers that we can't find, rapists, burglars, bank robbers. OJ can't find his wife's killer :->
It's not like there are 12 million people out their with little transponder chips that identify them as illegal immigrants. And all they needed was a half-decent birth certificate and they can get driver's licenses and social security numbers -- and after that they are indistinguishable from you and I (that is, if you and I were legal immigrants from mexico).
You can catch mice in your house if you give them something they want, like cheese.
You can "catch" the illegals already in the country if you give them a reason to be caught. Temporary worker program is something we can give them. A chance at citizenship is another thing you can give them.
If the only thing you offer is deportation, it's going to be hard to get them to give up. The I.D. program is a great idea in the long term, but it's not going to happen tomorrow. Border security can stop new people, but does nothing about those already here.
Yeah, but ... after you catch the mice you don't invite them to stay and breed and bring all their friends ... ! You kill the mice and dump their bodies. [Not that I am suggesting killing illegals ... but the point is to get rid of them.]