No it won't. Mass arrest of all demonstrators on May 1 should yield good results. Documentation of school children will work, checking for citizenship for every pregnant Mexican woman who wants to have her baby delivered for free at county hospitals, implement a national ID system, and push real enforcement of existing immigration laws. You capture 25%-30% of them and deport them and the others will get the message.
What you don't do is say things like "Gee, how would we deport 11 million illegals?"