The lack of desire to assimilate into our society coupled with the sheer numbers is the main problem with the southern influx in my humble opinion. Do european or asian illegals refuse to learn the language in such numbers? The answer is no. The logical question is why?
I think the reasons illegals from Mexico and S. America don't learn English are a) they have no intention of remaining here -- they want to earn some money and then go back home; and b) they don't need to learn English to get by because it's to the point where almost everything is bilingual. There are Spanish radio and TV stations, food labels, and on and on.
As far as assimilation of others, I think Asians want to remain here and fit in, and Europeans don't have to do much to assimilate. Most of the time we don't even know they weren't born here until we speak to them.