One single step won't do it. They'll need to beef up interior enforcement, allow the IRS and SSA to coordinate databases to ferret out the duplicate, phony, underage and stolen Social Security numbers. Additionally, go after Visa over stays through a beefed up system and the ITIN users as well. Punish to the fullest extent of the law employers large and small. Concentrate on industries like meat packing, restaurants and construction that typically attract illegal workers. Shut the businesses down and jail the owners, make hiring illegals as one of the just causes to break the Corporate and LLC's veils of protection so the businesses they affected can sue them and the owners personally. It can be done.
Go back to using local police. Immigration is a lcoal issue, the local cops know who's illegal, let them do their job. Cover their costs. Bank robbery is a federal crime. Who do you think makes the most bank robbery arrests? Local cops 10 to 1 or more. Same same with drug trafficking. And most other federal crimes. The local law is Border Patrols best but underutilized asset. We're fighting this crime wave with one hand tied behind our back.