The part of Brady that you donated to is a 501(c)(3) educational organization which means the donation is tax exempt. This isn't (or at least shouldn't be) the same organization that lobbies Congress, though they may be controlled by the same people.
If you want to make a tax exempt deduction to the NRA, you just need to make it to the NRA's 501(c)(3) which I believe is called The NRA Foundation. Remember though that 501(c)(3) groups have limits on what they can spend money on. If you want the NRA fighting for your rights in Congress, then you need to donate to the NRA-ILA. If you want them getting pro-gun Congressmen elected, then the NRA-PVF. If you want them to pursue litigation, the NRA Civil Defense Fund. Finally, if you want them to build ranges, teach gun safety and gun classes, that is the regular old NRA that most of us joined.
During the 1990s, the NRA was audited by the IRS on a pretty much continual basis thanks to a hostile administration. Meanwhile, organizations like the Million Mom March openly violated those regulations and got away with it. Eventually the MMM got too brazen though and got caught with their hand in the cookie jar (and our own Jim March was a big player in that). You can read the story over at TFL (circa 1999-2000). With a new administration coming to power, the original MMM basically allowed themselves to be assimilated into the Brady Campaign rather than face the music.