I thought the (excellent) movie "Act of Valor" pointed out the other way this issue could be resolved. In the movie, terrorists use the people smuggling networks to allow suicide bombers into the US, targeting a few stadiums in Southern cities. This is not the first time enemies of the US try to smuggle people in illegally - the Soviets and the Cubans especially sent many agents that way, as well as infiltrating US criminal organisations (see for example Oleg Kalugin's biography [1] which explores the links between the Soviets and the Italian mafia).
In the real world, no criminal organisation would be mad enough to let that happen (much as gangs in Mexico try to avoid killing gringos) because it would mean a promotion from "criminal organisation" to "effective terrorist organisation" and we saw after 9/11 how the American public reacts to that. So long as you're "just" smuggling drugs and people, it's "just" the DEA and ATF and the odd border agent.
If they did facilitate terrorist attacks, you can bet there'd be an enormous appropriation and militarization of the border, coupled with a systematic destruction of virtually all smuggling networks on Mexican soil and maybe temporary occupation of the territory south of the border. Panama was invaded for less.
But this is not going to happen just because a few people go on strike, especially when the majority of manual labour (11m vs 3m) appears to be illegal already without much outcry from the public which tacitly understands that this is key to cheap food and service.
[1] http://www.amazon.com/First-Directorate-Intelligence-Espiona...
As the CIA found in its paranoid early days, over-suspicion is highly counter-productive (see e.g. [1]). You just HAVE to trust your managers. Even if all services have some kind of internal intelligence setup to watch the watchers, it's focused downwards where the risks are higher and cost of suspicion lower, and it has to be run by people you trust the most. You balance the cost of a mole, versus the opportunity cost of turning down genuine defectors and trusting your own staff.
This is why (according to [2]) many European services are run by people from wealthy, old families, preferably with at least a few members who have served. It's expected that on average, these people have profound ties to their country - if nothing else, in the form of immense property portfolios - and thus are much less likely to defect. You can't bribe them, you can't offer them a better life [3], what's left? Ideology, and that can be somewhat watched for. Of course, you deny yourself some great talent that way but as with managing a hedge fund, you want to limit downside rather than maximize upside. Nationalism and dynastic politics are a form of defense against foreign enemies.
Hence Philby. He was trusted by design, not because MI6 were "bloody incestuous fools" or whatever, and no amount of surveillance would have changed that.
[1] http://www.amazon.com/The-Main-Enemy-Inside-Showdown/dp/0345...
[2] http://www.amazon.fr/Missions-methodes-techniques-speciales-...
[3] Kalugin recalls in http://www.amazon.com/First-Directorate-Intelligence-Espiona... that he was somewhat worried about Philby's living conditions in the Soviet Union (unheated flat, alcoholism, etc.). It's been a while since I read the book but I recall he or someone else decided to push for him to have a good quality of life as an advertisement to other potential defectors; only then was Philby put up in proper accommodation and welcomed by the Soviet system.