Obamacare prevents any gun registration.
Amendment 3276, section 2716, part C. supposedly says that there cannot be any collection of "information relating to the lawful possession of a firearm or ammunition".
So until the Senate and house change the law, registration is, for now, illegal.
This doesn't, of course, prevent confiscation or limitations on magazine capacity, nor making guns with certain features illegal.
Via Breitbart, HotAir and CNN.