The vast majority of people that cross the border illegally don't do it to mooch off of the social systems. People that unmotivated tend to not to bother leaving the comfort of their own home.
And many others from immigration heavy periods didn't, at least not at first. Due to the natural development of ethnic pockets, it was possible for quite a few immigrants to only have to learn a smattering of English, if any at all.My great-grandparents, great-great-grandparents, even one grandfather, came to this country from eastern Europe legally. They immediately set about integrating into the American culture, while still maintaining many aspects of their own. They learned to communicate in English without losing their native language. And they became American citizens as soon as they could, proud of their adopted country.
Yes, the politicians trying to give illegal immigrants the right to vote is purely a self-serving measure. We are inundated with illegals because the legal requirements are extremely restrictive and there is a very strong desire to immigrate. The desire is strong enough that there are immigration problems throughout central America as people push north. However, short of possibly shooting them on sight, it isn't going to be possible to stem the tide as a lot of them feel they have little, if anything, to lose.That's they way this country was built, and that's how I think it should continue. But now we are being inundated with illegal immigrants and our politicians won't do anything to stem the tide. In fact, they try to make it legal for these criminals to vote, just so they can be reelected! Shame!
The best solution is probably going to be one that no one likes. Personally, I think we should have a "yellow card" or second class immigration to go with the standard immigration along with a "touch home" policy like there is in Florida. Immigrants would be freely admitted as second class if they were in good standing with their country of origin (No significant debts, outstanding warrants, felony convictions, etc). In exchange for this easier entry policy, they would be required to attend and progress in ESL classes (unless they can demonstrate a certain level of English proficiency), have restricted access to social services until naturalized, and a somewhat longer naturalization time. Felony convictions or failing to progress in the naturalization process leads to a quick trip back across the border and revocation of their eligibility.
The benefit to this is that it gets everything above the radar (which means taxes get paid, licenses get issued, etc), and finds a less disruptive way to channel the issue.