You have to be a student of politics for a long time to see the effects of party over personal leanings of members within a party. There are example upon example of where an individual member of congress went with a party line vote. Voting the party line gets you membership and leadership positions and many other benifits.
As far as how the NRA handles this issue? I assume they understand politics as well as the laws of operating as a lobby for the 2,nd ammendment. I also assume that given these understandings that they are doing what they can do in the manner they are allowed under the laws.
I have no expectation that these circumstances will result in anything that looks like common sense to me.