Illegal immigrants are pouring into this country, not because we do not have the ability to prevent them.
Our politicians simply lack the will.
And a large part of that is the liberal socialist idiotarians on the left - imagine the response of the ALCU/CAIR and all of the Sheehadis and Bennishes if we attempted such a thing!
We'd have to deal with them before we could take any meaningful steps in the direction you propose.