Illegal immigration will be a problem so long as there is money to be gained by employers and illegal migrant workers... Money for the employers because they do not have to pay insurance on the people or claim their work on taxes, nor do they have to pay to modernise (as in farming industries), and money for the illegals because they get paid for their work in cash money, and don't really care what it is they have to do to get paid because they came from an impoverished area, and need to make real money in order to sustain themselves and their families. 
As well, there's no official language in the USA.  Want proof? Try living in Miami for a week, then, try Louisiana, and then, Texas, Alaska, Nevada, and about a half-dozen other cities on the west-coast. 
If you don't have to deal with the people that come into the US, legally or otherwise, what business of  yours is it what language they speak? 
The problem isn't that these people are taking away american's jobs, it's that there are some things that americans won't do... that creates an opening, and that friends, is where the illegals go. Try picking strawberries or lettuce for a week on end, and see how eager you are to do it later... the reason you can even get strawberries that have been mass-produced is because of illegals working in factory farms, and dealing with the same share-cropping BS that negros and indentured farmers had to deal with 150 years ago. 
The issue isn't the illegal immigrants, its the greed and ease of which people can make money off of the work of others that have no other way of making money. 
I'll give you 2 short stories, and leave it at that. 
1: A white, young and strong lad and his 3 brothers live in Ireland in the 1800's, and, unable to get work in the homeland, go to america to see if they can find fortune.  Well before the Civil War, they're contracted to a public works project in Louisiana, where they are literally worked harder than any negro or indentured servant (ie slave)... Literally worked TO DEATH because of malaria, typhoid and cholera, they're not even buried or committed decently.. they're put in a mass-grave and the employer keeps their wages as burial money.  Why does this happen?  They're Irish of course, they're lazy, but plentiful, and they spawn faster than rabbits which means an endless supply of cheap labour, and, they're dirty catholic whites anyhow, who cares about them?
This was the story of my Great-great uncles. They were treated like trash because they weren't Americans, and they were seen much as mexican labourers are seen now: expendible and burdensome. 
2: I'm a young, white, educated and professional adult, and I want to work for a company that wanted me to work for them, in the USA. I'm Canadian, and I use my work visas to their limits, and after that, I have to either get a signed contract, or a green card to work in the USA further.  I'm a contractor, and the company needs me to get a green card before they offer me a contract of employment. 
Where am I left?  I get to apply for a green card but, I have to be a resident.  In order for me to be a resident, need to be working in the USA because I can't get a lease on a place unless I'm working.  I can't get work in the USA because my work visas are expired, and I have to wait for 6 months before I can renew them. 
Basically, I got shafted out of a job I was fully (actually, over) qualified for, because of the absurd residence/work restrictions the INS was imposing on ALL non-americans.  
It's easy enough to bitch and moan about illegals, but they're doing a job that Americans won't do, and until you know what kind of hoops you have jump through in order to legally get work in the US, your belly-aching about "DOING IT LEGALLY" isn't finding a lick of sympathy here. 
Transeat In Exemplum: Let this stand as the example.