There are organizations opposed to NRA-style policies, but they aren't anywhere near as well-known or powerful. Why is that?
What has prevented the growth of an anti-gun lobby as powerful as the pro-gun NRA?
To supplement the other answers on this question:
One of the factors is that if someone were to advocate that strongly and effectively, they would (and sometimes do) face intense intimidation pressure and threats from people who are very passionate about making sure they have the right to own and use their guns however they want. Such intimidation does not need to come from the leaders of the NRA but can be effective coming from ANYONE who supports their ideas.
Edit: To those who think this sort of thing just doesn't happen, remember folks like Thomas C. Wales, and recognize that even the US President openly suggests that "second amendment people" should take matters into their own hands to remove someone from power if she does not share their ideas about how freely guns should be available.