I don't know about the NRA. I do know I don't support tougher regulations in any case.
I don't like the current background check requirements. For one thing, I believe that once a person has done their time and completed all obligations of punishment, all rights should be returned including the right to self-defense. For another I don't believe it is anything but an actual record which is being maintained despite all claims otherwise, IMO a pseudo-registration.
I am not an advocate of allowing access to all forms of weaponry. I am on record as arguing the 2nd Amendment does not apply to area effect weapons (like flamethrowers, NukeBioChem), munitions (grenades/rockets/demolitions), crew-served weapons, weapons platforms (tanks, battleships, fighter jets). I think they are reasonably limited to the basic arms and armaments a common infantryman would be kitted with for everyday service.
Every time I hear about "reasonable" controls I see how they don't seem to work, thus leading to MORE "reasonable" increases in controls. Right up until the ultimate control is licensed ownership of fluff like those German "starter pistols" I've heard something about, all bark and no bite.