Marta,
your reasoning, and your choice of words, are disturbing. For instance, why the gratuitous addition of "non-English speaking"? And your reference even to legal immigrants? Are you of the opinion that they too should be dealt with in some way? And as for your reasoning, it seems immediately obvious to me that it can be recursively applied to disabled people and further on to other groups.
The issue should not be the consequences of an overburdened system but the causes of it. If, as Doug has pointed out, immigrants have a net +ve contribution to national wealth, then they are helping solve the problem, not worsen it (note also that the negation does not necessarily hold). We have to look farther than the scapegoat to find the real causes.
Perhaps I am reading your opinion improperly, having entered the conversation midway?
--ravi
P.S: I see no differentiation between legal or illegal immigrants, myself. I mention it above since those to the right of me, in this case, it seems Marta, often do.