Good point, and not too bad of an analogy, either. The difference is that we're dealing with human beings who should ideally be able to organize & change things, rather than cats responding simply to instinct. Education can change humans; we have the power to affect our destinies.
I do like the cat analogy in the mention of following the food source. It's irresponsible to continue to allow the influx of immigrants without addressing the root of the problems in the nations of origin, just as it is pointless (though it can be gratifying) to feed a stray colony without addressing spay/neuter and immunizations. You're right - as long as there is desperation at home, people will try to get to the food source. The Mexican people who succeed in the U.S. and return to try and improve the desperate situation in Mexico can (sort of) be compared to test/spay/neuter release programs in feral colonies. Or is that too much of a stretch?
Hopefully they can make a difference in their home countries, so that people will stop abandoning family, friends and country, risking their lives to get to the U.S..
*As far as America's immigrant history goes, yes, I'm sure that the Native Americans (who were also immigrants waaayyy back when, too) would have loved it if everyone else had stayed away, but what's done is done, and it may be sad, but I'm worried about the future - and everyone's future, too. Things need to change in these countries - there simply isn't enough inhabitable land left to accommodate an endless influx of people, and still allow us to be the world's breadbasket, too.
My worry is that if things don't change in these desperate countries, and we don't change our policies, that we'll end up in the same boat - then where will people go for refuge?