I'm a software developer whose career has been ravaged by the H-1B visa program.
One strong argument you can make against non-immigrant visas and illegal immigration is the sad state of health insurance in the US. If there really was a "skills" shortage, employers would be offering health insurance and lower copays. But in fact, the opposite is true. Fewer citizens have health insurance and for those that are lucky enough to have this benefit - the copays keep increasing and taking a bigger bite out of the paycheck.
IF THERE IS A SKILLS SHORTAGE, THEN WHY AREN'T EMPLOYERS OFFERING BETTER BENEFITS, LIKE HEALTH INSURANCE, TO ATTRACT EMPLOYEES?
This article on bloomberg.com provides further proof.
The article, "American Workers Rejecting Jobs as Immigrants Drive Down Wages " by Heidi Przybyla, quotes George Borjas,saying "The idea that somehow you have a need for people to do jobs that Americans won't do is just insane," and continues by noting that it's the low pay and lack of benefits that drive natives away.
Bloomberg's owner, New York Mayor Michael Bloomberg, has said illegal immigrants are good because they maintain his golf course. (I'm not making this up). Now maybe he'll read his own news service.