At some point legislation on this issue was going to reach critical mass. Now is the time for the 'majority of Americans' to voice their opposition and compel big changes to any legislation before it becomes law.
The only way I can think of is to stop funding the Republican Party across the board. Every time you get a phone call or something comes in the mail let them know you will not give them 2 cents until they take real action on immigration. That is what I have been doing for months.
I get a call, they give their 'we have to fight the Democrats' speech and can you please send us $100. I respond, do something about illiegal immigration and then call me. If we can get enough people to multiple that response they will get the message.
Maybe start a web site - stopgopfunding.com?
Oh, they get it, he's just saying, "screw the American people, I'll do what the hell I please".