" the NRA seem to oppose ANY restrictions on gun sales"
If that were true the NRA would be advocating the removal of NFA restrictions (military weapons), ending background checks, restoring the right for violent felons to own firearms. I think we can both agree that isn't correct.
I assume you probably mean oppose "any NEW restrictions"? I can't speak for the NRA but I know many gun owners are wary of so called "reasonable restrictions" which are neither reasonable nor effective.
Waiting Periods - proven ineffective and infringes upon population which may be most at need of personal protection
Gun Registration - expensive and utterly useless for solving crime. Criminal are automatically exempt. In countries with registration schemes it is often ignored.
The one area where the NRA is wrong is in not supporting Universal Background Checks however understand this isn't some magical solution. There is little evidence to support this would be more than closing a common sense technicality and would most likely have no statistically significant effect on homicide rate, number of mass shootings, accidental deaths, or suicides.
I think improving NICS and finding ways to make it easier to flag mentally ill persons would be more effective but the later is tough to do and requires a radical change to mental health in this country. It isn't a nice soundbite like "ban assault weapons" and would be expensive and a long term strategy but it could help significantly.
So what new restrictions would you like to see and what effect do you think they will have?