It would work if we work to secure the border.
Now there's some critical analysis! The reason the border is insecure is because so many are willing to cross it, and they're willing to cross it because they know that nothing happens to them once they get three days past the border. Illegal aliens are free to roam the country until the next poltical snake oil salesman says, "we better legalize 'em, no other choice."
Rinse and repeat.
We can make the border more secure, but we won't ever have the manpower to lock it down tight. That's as unrealistic as saying we'll deport them all.
Are you a doctor, a lawyer, or both? Ever hire a nanny?