I don't think it would be. Walls aren't hard to get past if there's nobody around watching it. Going to permanently station tens of thousands of troops on it also?
I looked into this a little in college. I forgot the price though unfortunantly. What it looked like was essentially this....
You actually have two fences or walls, should be 12-20ft at least tall. One on the Border and another either a mile to a mile and a half from it. Both fences/walls tops are slanted at an extreme angle southward, with barbed wire. This would make it far more difficult to scale as one would need to somehow get over this lip.
The Mile and a half area between both walls would be essentially cleared so as to have little to hide behind. You place periodic cameras along it and, depending on price and budget, sensors on the wall and/or ground for movement at more heavily trafficed locations.
You position a station every 60 miles, giving you roughly 33 stations. Each station is responsible for manning a 60 mile strip, which would be done with 3 vehicles for each location manned by two Border Guards. One car 20 miles to the east, one car at the station, one car 20 miles west. Each car is responsible for 10 miles to either side of it, and the side cars can also act as additional support for the next station if needed. Assuming most of the people crossing are not going to be amazing runners, some with families, we'll give a rough average of 10-12 minutes to cross the distance. Going 60+ MPH the cars should be able to arrive prior to the alien is able to pass into the US.
Assuming 4 shifts this would account for just under 800 border guards. If you wanted to add 2 more shifts worth of people and give each station a support vehicle that could be deployed wherever it needed it'd be just under 1,200.
If you wanted to go on the safe side, and do the 6 different "shifts" of in the field guards, you could do 14 officers/managers/admin/operations type people in each station location to bring the station total employees to 50 and total employees to 1650.
With this you'd have a few things...
Two difficult to climb walls.
Guards maning essentially every mile of the border.
Technology assisting in early detection of crossers (with cameras and motion sensors).
Would it be perfect? Absolutely not. There's still the potential for tunneling though you don't expect a mile and a half long tunnel under the entire thing, and you'd hope the guards on patrol would notice tunnels coming up in a barren middle zone. I'm sure there's other ways to definitely work around it. However it would be a hell of a lot more secure then it was previously and while it won't stop the incentive for coming it'll hopefully either stop or deter a decent amount as we work on the next phase.
Throughout that area of course you have your normal legal border crossings as well.
While the numbers of individual employees seems large at first glance it'd still be miniscule compared to many other law enforcement agencies within the country. The cost of building would be relatively expensive, I say relatively because it'd be a great deal cheaper then what the government's been spending on some things lately, however it would need to be weighed against the amount of money it could potentially save through decreased illegal activity within the country as well as the national security benefits of further ensuring that we have a good chance of knowing anyone who enters the country and to make the drug trade more difficult.
This is just a rough sugggestion, no I do not know details, no I've not looked into it greatly for some time now and even then it was only a 2 week long project. But that'd be my initial thought.