There is no question that every immigrant wave has brought productive honest people, moochers, and criminals, in different proportions. There is also no question that our public benefit system makes it easier for the second category today, as oposed to 100-150 years ago. The question is as to how to make the system work to get the highest proportion of the first,and the lowest of the other 2. But claiming that few or no illegals are working and not commiting crimes (and simple illegal status is currently only a civil offense) is just not true.
In fact, there is often a blatant contradicition between the claims that ilelgals are all sitting around on welfare and the claim that they are all taking jobs from hard-working americans who are unemployed because they can't find work beaccuse the illegals have taken it all.
Noncitizens in the Federal Criminal Justice System, 1984-94
"A study by the Urban Institute estimated that approximately 86% of the illegal aliens living in the United States are concentrated in seven states: Arizona (1.7%), California (42.6%), Florida (9.5%), Illinois (5.2%), New Jersey (3.4%), New York (13.2%), and Texas (10.6%). The Institute estimated that 2.8% of the combined population of these States are illegal aliens (Rebecca L. Clark, Jeffrey S. Passel, Wendy N. Zimmermann and Michael E. Fix, Fiscal Impact of Undocumented Aliens: Selected Estimates for Seven States, The Urban Institute (September 1994).)"
http://www.ojp.usdoj.gov/bjs/pub/pdf/p03.pdf had no useful information regarding illegal aliens in California prisons. You'll have to forgive this old reference that the DOJ used from the Urban Institute, but if California had a population that was 42.6% illegal alien a dozen years ago, it would not surprise me that, all other things being equal, that their numbers now approach 50% in California prisons.
Add to that folks with an ideology of reconquista, no interest in assimilation, aliens being responsible for 55% of multiple drug resistant TB in this country, a higher risk for chronic diseases such as asthma, high blood pressue and adult onset diabetes mellitus, the latter two being associated with higher risk for coronary artery disease and stroke, with their worse morbidity and mortality being associated with a putative hidden bias or indifference by the health care profession, well this doc says no thanks.