Building a wall and hauling people off to camps won't really cut it though.
It would work just fine.
Don't just "haul people off to camps", though. We don't want them here. Period.
Follow that up with deportation within 48 hours of arrival at the camp and you have a winner.
Actually it wont. For starters no nation has successfully defended its border by putting up a wall that size. It is impossible to police it all. Second, you can deport them back to, e.g. Mexico. Then what? They will simply sneak over again. It is impossible to secure the US from ilegal immigrants without turning the place into a police state.