That is not very realistic. It would be nearly impossible to round up all the immigrants and deport them all. There are too many and they are spread too far and wide. We certainly should be checking those who are emigrating here though. This particular family apparently emigrated to America a very long time ago, like 17 years ago I believe they said.
First, mass deportation of arab muslims is quite possible, and after another, inevitable major attack like 9/11 with thousands dead, many americans will demand it. As for mass deporting illegals, that should have been done already, as Eisenhower did in the 50s. When millions of americans are living in tent cities unable to get jobs while illegals work, you will see an uprising in the US not seen since the 1860s civil war. 2 different topics...