If the wages that illegal immigrants are being paid are so terrible, then why do they come here? And why would they stay when they do? The answer simple: they can live a better life as illegal immigrants here making less than minimum wage than they can if they stay in Mexico. Offering someone a better life in exchange for economic benefits to the entire country doesn't really sound like exploitation to me. It's more like a mutually beneficial agreement.
The point is, the people who believe illegal immigration is an economic issue are on the wrong side of the facts. There are numerous studies that indicate that illegal immigration makes us more wealthy as a country. Back in 1980 before the most recent flood of immigrants it was well-established amongst economists that illegal immigration was good for America, then there was a wave of massive immigration during the 90s (accompanied by massive economic growth I might add) which had no observable negative impact on the economy. The data simply isn't there: they took our jobs doesn't pan out.
As far as whether or not this would help the poor: I doubt it. You say people need to cut back, do you know what would happen if the middle class did that? Less demand plus higher prices and increased frugality equals fewer jobs. The very jobs we're discussing here are products which are sold to the middle class. Lets see, less demand and more cost per laborer; how exactly does that add up to helping the poor? Remember, the 3-8% increase is amongst people who didn't finish high school, not John Doe who got laid off by Boeing after working as an Engineer for 15 years and can't make his mortgage payment.
I wonder where the poor are going to get the money to relocate to these jobs (travel expenses, finding a place to stay, et cetera), considering the majority of positions that illegal immigrants take that have been discussed on this thread exist in the countryside and rural areas.
None of this even argues the practicality of any proposal. Did you know that the Mexican border is 3141 km? Building a fence would be one of the largest construction projects ever undertaken by the United States, and policing it so that people don't simply climb over it or dig under it... well, that's another problem. Then there's the fact that a large portion of illegal immigrants are the type who come here and simply stay after their visa expires...
So lets see, it benefits us economically, it would cost us in both GDP and wealth to get rid of it, furthermore it would require more laws, government spending, and government power to actually enforce a ban on illegal immigration. I have a feeling if I ever figure out why the conservative party in the US is against illegal immigration, the answer will have 42 letters.