Up until about 1975, the National Rifle Association was all about marksmanship and training, shooting ranges and safety. The NRA supported the 1934 National Firearms Act and the 1968 Gun Control Act, but with the passage of the '68 GCA, there began to be some pushback within the organization.
"Gun control" is promoted as a "public safety" issue, but it's never really been about safety, it's been about control. Specifically, it's been about keeping guns out of the hands of The Other. The best example of this I can cite is the 1857 Supreme Court Scott v. Sandford decision, in which that court declared that Blacks - free or slave - could not be citizens, because if they were:
It would give to persons of the negro race, who were recognised as citizens in any one State of the Union, the right to enter every other State whenever they pleased, singly or in companies, without pass or passport, and without obstruction, to sojourn there as long as they pleased, to go where they pleased at every hour of the day or night without molestation, unless they committed some violation of law for which a white man would be punished; and it would give them the full liberty of speech in public and in private upon all subjects upon which its own citizens might speak; to hold public meetings upon political affairs, and to keep and carry arms wherever they went.
New York's 1911 Sullivan Act, requiring a license to own concealable firearms, was also passed as a safety issue, but most recognize it for what it was - a law that made disarming immigrants legal. And statistics indicate that firearm-involved homicide in New York City increased after its passage.
So the membership of the NRA began to realize with the passage of the '68 GCA that the end game being pursued wasn't "public safety," but public disarmament in the name of safety. After all, the argument promoted by gun "control" advocates is "more guns = more crime" and "the number of guns is the problem." Carry that logic through. If "the number of guns is the problem," then ipso facto, decreasing the "number of guns" must be the solution, no? And how much decrease will be required? Well, how many "gun murders" are you willing to accept, comrade? It seems pretty obvious that for gun "control" advocates the acceptable number of guns in public hands must be statistically indistinguishable from zero.
In 1977 the portion of the NRA membership that grasped this concept became high enough that during their annual meeting that year they elected a board that also grasped the concept, and the NRA got directly involved in combating further "gun control" measures through legislation and public awareness efforts. Each gun control success such as the 1994 "Assault Weapon Ban" (that wasn't), became a recruiting issue for new NRA members, since the ACLU has stated in no uncertain terms that it does not consider the Second Amendment to the Constitution a protection of an individual right to arms. That has been their focus ever since, though they are still the primary source for training, support marksmanship and competition, and work particularly hard at keeping ranges open.
As a result, the NRA has at present a paying membership of about five million, it represents tens of millions more, and they VOTE. Since Job #1 of politicians is "get elected," and Job #2 of politicians is "get re-elected" with Job #3 being WAY down the list of priorities, being able to deliver millions of votes gives the NRA massive political clout. Bloomberg can give money, but so far he hasn't been able to buy many votes. The Joyce Foundation has been throwing good money after bad for quite a while now.
Gun "control" organizations such as The Brady Campaign, the Violence Policy Center, Moms Demand Action (a wholly owned subsidiary of Bloomberg) et al. may deny it all they wish, but the NRA follows a grassroots movement - it doesn't lead. A lot of people had understood what was going on prior to the passage of the '68 GCA, but they weren't members of the NRA. It's just that now it's the 800 lb. gorilla in the room that no one can ignore, and it's the target of blame for the media because they have nothing else to point to.
If you're really interested in the subject, I recommend the book The National Rifle Association and the Media: The Motivating Force of Negative Coverage by Professor Brian Anse Patrick. It's pretty much a PhD thesis with all the appropriate buzzwords of a narrow academic discipline, but the information in it is pretty fascinating, and its conclusions were - to me - quite surprising.