Not if you cut off social services to non-citizens so they will self-deport. We won't be able to do that once the illegals are citizens and unemployable.
Right now some business have to employ illegals to be able to compete with rival businesses that also employ illegals. If we tell businesses that those days are over and anyone emloying an illegal will face jail time then it will all stop. Most businesses won't suffer as the competitors will be under the same rules.