What works.

One of the groups to which I belong, the IEEE, has for many years pushed grass roots efforts to help the plight of U.S. engineers (with a little bit of schizophrenia, as they also have "international" in the name, and have explicit ties to helping engineers world wide). It should come as no surprise that they publish books on how to influence the legislative branch. The one way that works best is to visit in person. You have to visit your representatives, but that has more effect than any other method. I am going to Washington in two weeks if I can get an appointment. The immigration issue is worth it.