What has made "the NRA"---really, gunowners, the NRA has but a fraction of them as members---so powerful?
Well, first of course there's a lot of us. Even having only a fraction, the NRA now has 5 million members. The EFF? I would be surprised to learn they had more than 50,000 (couldn't find a number in a quick search).
2nd, we vote, and many of us vote first and foremost on this issue. Especially since it's a good general touchstone, not that more than a tiny tiny fraction of national level politicians really give a damn about either issue no matter what they say most of the time.
3rd, there are many major elections where it's clear gunowners were a necessary if not necessarily sufficient part of the winning side. Gun control at the national level mostly disappeared in this century until Newtown after the Democrats suffered a string of catastrophic defeats from losing both houses of the Congress in 1994 to Al Gore losing by a whisker in 2000. That it was even close is telling, especially since Bush isn't much of a conservative or friend to gun owners, e.g. he officially supported renewal of the "assault weapons" ban.
(Note that it's in our cultural DNA to defy being told we can't or shouldn't have something, be it guns or e.g. drugs. But those are tangible, literally put your hands on them things, not like "privacy", the loss of which isn't immediately visible.)
On the side of the Stupid Party, every post-Reagan defeated Presidential candidate was, or appeared to be bad on gun ownership (Romney's actions were good, but his rhetoric was very bad). Again, the very narrow margins by which Bush won in 2000 and 2004 are probably also telling, bad rhetoric and very few good actions.
Now for some historical specifics that made a difference:
The biggest is how extreme gun grabbers are. While businessman Eric Schmidt is notorious for some creepy even if possibly true statements, I'm not aware of any national level politician who's willing to go on record saying we have no right whatsoever to privacy (whatever they actually believe).
Nothing compared to e.g. Dianne Feinstein's "If I could have gotten 51 votes in the Senate of the United States for an outright ban, picking up every one of them . . . Mr. and Mrs. America, turn 'em all in, I would have done it. I could not do that. The votes weren't here.", or Michael Dukakis' "I do not believe in people owning guns. Guns should be owned only by police and military. I am going to do everything I can to disarm this state."
Legislation stripping us of gun rights are much more in your face than e.g. FISA, and have much more concrete results (see below). Privacy is much more a Federal issue, although there have been a number of gun privacy atrocities at the state and local level. Whereas the nation frequently watches some state go crazy and e.g. tell you that you can load only 7 bullets in your 10 round magazines ("clips"), and arrest people on that basis. Plus hypocrisy, there are many many carve outs for the anointed, be they police or politicians, or the frequent discovery that a prominent gun grabber owns guns. And all the politicians with armed bodyguards telling the rest of us we don't deserve that level of protection.
Then there are specific atrocities, cases well known by gun owners of innocents brutalized or killed by abusive organs of the states. This became big a while after the national Gun Control Act of 1968 was passed, when the BATF had to find something to do for its Revenuers after sugar price supports killed the moonshine industry.
Our side can point to kittens killed ("I swear I am not making this up"), pregnant mothers who miscarried, people crippled for life, mothers shot dead while holding a baby (Ruby Ridge, in which the BATF was enlisted to try to force her husband to spy), and many many outright killed (Waco started out as a BATF "ricebowl" operation, they wanted some nice video for their first budget in the Clinton Administration). Plus a constant drumbeat of gun owners ensnared by "flypaper" laws in gun grabbing localities; even NYC has realized it's damaging their tourist industry.
And how could I forget Fast and Furious, just one of several Federal Government gun running operations that sent thousands of guns south of the border, resulting in 350 deaths and counting, just to generate better statistics for gun grabbing propaganda (that reason is now on record and any other explanation suffers an Underpants Gnomes logical error).
The very secrecy of our national security privacy problems makes the latter problematical. Ignoring that the targets of the DEA are seldom ones we can empathize with, that they launder the tips they get from the NSA means that as of now I don't think there's a single specific case we know of.
And one final general point: lots of public figures are willing if not happy to demonize gun owners of almost every sort, and gun organizations (we can see the latter in this discussion). That results in strong push-back from the targeted (again, it's not in our cultural DNA to take that lying down).