Legal immigration has a comparatively small effect due to the fact that they're part of the skilled labor force and generally fill gaps in our society. The number of people actually holding H1Bs is so small that I find it hard to believe they have any major pull on the various sectors outside of the few firms that are known to be abusing the system.
Fixing the system in a humane way that also doesn't blow up the lower classes is a herculean task.