There have to be easier ways.... I'm pricing out the cost of used dry vans (those big steel shipping containers), especially the 40' ones that are 8 feet high. Placed end to end, it would take about 132 of them to create an ad hoc mile long wall.
The old roman trench and berm topped with a spiked wall might work too - the trick is to funnel them into smaller and smaller tracts of land, where you maximize surveillance and patrols....
This is why at least a partial physical barrier is absolutely essential to any mix of sensors and patrols.... because the perimeter is 1700 miles of open land and passable Rio Grande... It would take half the army to seal the border using patrols.... (you need boots on the ground to physically stop human wave assaults.... )
But by walling off 1000 miles of the easiest terrain, you automatically focus the flow into those areas where your limited manpower can be maximized.
In a sense this is like the Roman battle of Watling street in Britian - where some 10,000 legionaries held off 250,000 barbarians by focusing them into a funnel shaped battle field...
The BP did a study of a triple fence barrier system (currently runs from the Pacific to some 20 miles inland) and found it could be constructed for about $1m per mile. I think using Jersey walls as the anti-vehicle barrier and then steel or concrete wall /Bollard post + steel mesh fencing would reduce costs for a 1000 mile barrier running from the Pacific to the Rio Grande. Yes, a Maginot line, but it focuses crossings into relatively few points - tunnels sure - if you have the time and resources to tunnel half a mile (!), such as the border of Texas.
But that just makes the BPs job easier - focusing on the big gateways as well as the moated section along the Rio Grande.
But this makes too much sense which is why the government will never do it. If it cost $230b then they'd fall over each other trying to 'do it' but since we can easily build a wall across the entire frontier for a paltry $2b.... they'll never do it.