It's true that many of the illegals are Mexican. But there are a lot from other countries - Ireland has a surprisingly high number.
Many of the illegals from all countries came here with valid visas, and just overstayed. Many people think at least half did that.
And it's true that a lot don't really want to become Americans. They just want to work here until they have enough money to live in their home country. Did you know that there are large colonies of American retirees in Mexico? If Mexico was such a "hellhole" (have you ever been there?), why do so many American retirees move there?
I have been to Mexico. The resort areas are fine (Including the retirement enclaves). The country as a whole is corrupt and businesses cannot create jobs or people even start a business with out knowing someone and bribing the right people. However, I do think we should have the same immigration laws as Mexicos'