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Turns out all we had to do was wait for it to get to the US Senate. Unless it is something to keep them from waiting in line at the airport due to delays caused by the laws THEY passed, the odds are against a bill even being able to get an up or down vote. In this case, it worked out for the better and it looks like CISPA is not going to happen anytime soon.
I know it can feel like Don Quixote tilting at windmills, but basically you can do the classic things: contact your congressman and senator. As the tweet you mentioned suggests, the voice of individuals may not mean much to a lot of politicians compared to corporations with a river of cash, but it is still the best option we have. You could also donate to the Electronic Freedom Foundation, the main organization who fights this sort of thing, I suppose. Speaking of the EFF, they have a link where you can contact your congressman/senator, but I think a telephone call and/or physical letter is more effective. Still, it's better than nothing. Oh, and I also suggest you remember what they do when you are in the voting booth next election.