Please don't get caught up in the "once we enforce the border everything is ok" nonsense. Banks enforce their borders. Wal-Mart enforces it's borders. Banks get robbed and people still shoplift.
If the message was: once you get the money/merchandise off the bank/store property it's yours to keep then we would have a lot more stealing.
The key is reducing the incentive (think signs that indicate there is less than $50 in the cash register) and punishment after the fact.
Our border should be "secured" but it is impossible to design a foolproof safe let alone miles and miles of border if what is on the other side of the barrier is a strong enough pull for criminals.
The term we are looking for is "interior enforcement." The simple method of requiring names to match the SSN for a bussiness to claim the employee as a tax break is the biggest no-brainer in the world. Requiring the same for any social services, drivers licenses, banking, etc is the next step.
We can't arrest all burglars in one day just like we can't deport all illegal aliens in one day. But we can arrest and deport them when we find them. We can put up a big sign that says "only $50 in the safe" to reduce the incentive for them to come here and break our laws.
Or we could go the Clinton/Reno method...