Enforce eVerify. Done.
Harshly fine/punish employers for hiring illegals and the jobs dry up and the illegals begin going home - while the ones that wanted to come here realize it would be pointless.
This is also much tougher to demagogue since the punishments fall on corporations (that the media consider evil anyway) instead of illegal individuals, families with kids, etc.
Sure build the wall, we could use one - but strictly enforcing eVerify and going after companies that hire illegals would solve the problem at almost no cost.
Audit businesses for them having form I-9 and a copy of their photo ID and Social Security card as currently the law.
Arrest the owners of any business that doesn't comply and give them a heavy fine for a first offense and mandatory prison for a second offense.
there won't be a job for an illegal within 3 months or less.