To effectively close the border, you have to remove the incentive to cross the border illegally. One strong disincentive would be the confiscation by law of all property obtained in the United while unlawfully present and employed in the United States, punitive damages for the illegal immigration, and permanent deportation. Prohibition of future U.S. citizenship would also be necessary as a disincentive.
I am in favor of anything that is not cruel or unusual punishment. Those are standards of humanity, given from God, in my opinion, and they regulate all our lives. Except in times of war when chaos reigns, they are binding on a civilized person.