No, round up these people: the ones who are here illegally on expired visas. Send them back to their own countries.
You have to do this in phases. Phase one. Adopt the China policy to stem the flow into the country from the 20 nations listed by China. Include Israel. I love the concept of a homeland for the Jews but....this is America, my home. The Israelis have to be treated along with the rest to maintain fairness to the process. Jerusalem has to be an international city along the lines of the Vatican. Palestine needs to be a state by annexing part of Jordan along with the current real estate that has been granted to them. Until these issues are resolved and as long as the USA and Israel are in a state of war, stop entry into the country.
Phase two. Revoke the visas of persons from the 20 states along sex and age guidelines. If your a male between the age of 16 and 40 your on the list. Don't include Israel in this step unless Israel is found to be directly tied to a terrorist act in the USA.
Phase three. Process naturalized persons of certain national origin and provide them with their own security clearance documents. Use technology to make these documents verifiable. If this sounds like second class citizenship, well in a way it is. If the folks targeted for these security steps do not cooperate, encourage them to emmigrate at once.
This is all untenable under our present Constitution so I guess we are doomed.