Call your congressperson. They do care what you think, at least a little bit, especially if you take the time to call or write their office thoughtfully.
If your congressperson voted for the bill, you can express your dissatisfaction, which counts for something. This kind of thing is not the sort of issue your congressperson likely understands or even thinks about for very long - they just do what their staff suggest and they don't expect to be called on it when they get back home to their districts. So if you can make it an issue, make it something they think might affect votes, you'll raise the priority and raise the level of discussion a little bit. And that makes it harder for the kind of disinformation that spreads around CISPA to survive.
Congresspeople are currently very afraid of "getting SOPAed" where they try to make some kind of tech policy regulation and then accidentally set off a huge wave of activism.
Keep in mind, just because something passes in the House doesn't mean it's law. There's a long process - right now it's still just a bill (that they voted for on Capitol Hill (sorry)). There's a lot that can be done, and, now, probably will be done to mobilize on this issue. I doubt that it will come to SOPA-level activity (SOPA would have affected the bottom lines of big tech companies. This is "just" about privacy). But there's always room for trying to make things more reasonable.
Let's say the senate amends the bill, and successfully passes that. The house would need to vote on that modified bill.
Normally, once the two sides pass relatively similar bills, a conference committee is formed to resolve any differences, and then that resulting legislation is voted on.
I'm not from America, but, as an Internet citizen, I still care deeply about the issue. Can I just call American politicians to express my dissatisfaction? Does it count if I don't have a social security number? I already donated to Fight for the Future, is there something else I can do about this?
Call your congressperson. They do care what you think, at least a little bit, especially if you take the time to call or write their office thoughtfully.