I have heard the line about deporting too often. It has been repeated by all sides and that cements my thought that it is a lie. Prove to me it won't work.
Of course deportation would work. And you wouldn't need to deport them all. Start prosecuting the corrupt employers who provide illegal aliens with a job market, and the job market will dry up.
Then the illegals will go home themselves and new ones will stop coming. Combine that with Border Patrol round ups and deportations like last summer here in California and even more will go home themselves and not bother to come in the first place.