Your perception is wrong. The gun lobby is crazyily grassroots. The NRA is demonized, but their spending in lobbying is low (their income is relatively low and they have a lot of other elements such as training and certification) and less than the gun control lobby since Bloomberg (and some silicon Valley VCs) began to lobby.
There is only one reason the NRA has influence: members and sympathizers will vote on thier recommendations, they have a lot of members and the NRA will always endorse the most sympathetic candidate to thier cause regardless of party affiliation.
The pro encryption lobby could emulate this. Lobby groups like the eff need more members and crucially need members to vote for who they recommend regardless of the candidates other views ie. vote for Trump if he said he was pro encryption.