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.
OK, I'll get right to that point. We now have at least 10M (no one knows the exact number) Mexican and South American workers in this country. They're all over, not just in border states. They're doing jobs that American born citizens won't do. Please don't try to tell me that in areas where the unemployment rate is <4%, Americans are lined up to take jobs as busboys, hotel or office cleaners, or lawn care workers. Our economy depends on workers like those.
We can't replace them all overnight with 10M who have gone through a legal guest worker program. That would just give them, and their employers, more incentive to hide.
I don't see that we have any choice but to make it possible for these people to get some sort of legal status.
Our previous guest worker program limited the time they could stay here, made them leave dependents behind, and linked their stay to the job (they came for one job, and if they left it, or the job ended, they went back). Even more importantly, it made the employers responsible for the guest workers. Having employers keep track of guest workers is far more efficient than setting up a huge gov't bureaucracy.
So, to summarize, I do think illegals should have a chance to become guest workers with employer sponsorship, and with the same rules (limited stay, no dependents, and no path to full citizenship) as ones who would come here under a program.
Our economy and sheer practicality both make it the only reasonable way to proceed.