Fences don't eliminate the problem, except when they're new. It takes time to dig a tunnel, and as soon as the fence goes up, digging will start. (I'm not sure, but I think the latest tunnel we found does go under a fence).
Of course there isn't any way to reduce illegal immigration to zero. We've had that forever, and we always will. What we need to do is to get it to manageable levels. The best place to start is with a guest worker program. We had one in the past, and it worked very well. The only reason we stopped the program is because our "bleeding hearts" thought the workers were being treated poorly. Some probably were, but eliminating the program was a short-sighted solution.
If we had a legal way for the workers we need to come here, I'd be as harsh on illegals as you are. But we don't. And we do need them.
The latest one we found took six months to dig. Israel's fence has been effective for a longer period than that. Plus, we have equipment for detecting underground discontinuities. It's true that so far, there've been quite a few false positives because of naturally occuring underground features, but once those are all mapped along the border, then anything new would pretty much have to be a tunnel.
On top of which, there's just no way that the same levels of illegal entry can be maintained through tunnel traffic. Any house that serves as the terminus for a tunnel would immediately draw attention to itself if that level of traffic were to pass through it.
The best place to start is with a guest worker program.
I notice you keep avoiding the point about letting illegals become guest workers. That's the biggest point of controversy with the President's plans. You began this exchange by denying that there would be a conservative backlash resulting from this, saying that the issue is "complicated". But there's nothing at all complicated about recognizing that rewarding illegals with legal status, or even holding out the hope of doing so, makes the border much less manageable. There's no excuse for him doing that.
We don't need these invaders, we need to get our country back to some pride inits youth. Get the young ones away from the playstation and to a job.
Who cleaned toilets and cleaned dishes before these people came? Who cut the lawns?
We got along just fine without almost ten percent of the population being illegal aliens.