The number one argument against immigrant labor is that they will take job opportunities away from Americans and cause an overall drop in wages. However, this is probably the easiest misconception to debunk, as immigrants are more often inclined to settle in less populated regions and actually help increase supply and demand generating even more job opportunities. In addition, many studies show that immigrants usually just compete against each other for less-skill positions and companies keep favoring the hiring of locals.
Hope this helps!