The Bracero program was good economically, and cut down illegal immigration by over 90%. That's not to say the program didn't have issues (like abuse), but those are bugs we can work out. A Job is a zero Sum game, Jobs however are not, because when you get to the plural, you have to consider all the conditions that make Job creation possible.
Immigrants, even illegal ones, contribute to the conservation of Resources, they make labor costs cheaper, thus a businesses has more money to spend on other things, they can expand their enterprise, and hire Americans to do more skills-intensive work. Which is good, because most Americans aren't the low-skilled sort, they're in the middle, while immigrants are stratified into low or high. They compliment what we lack, and make more economic activity possible.