I briefed and helped Dave Brat after that. We put out over 40,000 robo calls in Cantor's district to expose him on immigration. Cantor was about to release the GOP version of the Dream Act. We also went after Goodlatte, but he backed down.
I went over the very same issues you did back in 1995 when something could be done about this in a meeting with Newt who had just become speaker of the house.....the meeting broke down & it ended in a nasty way. Suffice it to say I left that meeting with the understanding that Newt was an open borders guy & favored massive amounts of legal immigration.
He was still lying to the GOP base at the time about cracking down on this issue. As an addendum: I ran into Newt at a GOP get-together several years later, after he lost the speaker-ship, and I let him know in no uncertain terms that he blew the 1994 Republican Revolution...he made an aggressive move toward me, was stopped, and we then engaged in a shouting match which resulted in him trying to spit on me....such is the scum we spent years & money trying to elect to the GOPe.