Black
Of course I am for background checks.
One can own a fully auto 'machine gun', but it depends on a couple of caveats. The most important one is not being a 'prohibited person'. This is kind of your catch all felon, crazy, violent, etc. Then, it goes down to whether it is outlawed at the state level. Then, it also must be manufactured before 1986.
Thing is, these weapon rules are pretty much close to what you euros have. Prohibitive person. Full auto weapons here routinely run around $10K +. Combined with the taxes and government registration by the ATF, makes full auto weapons prohibitively expensive. Also, like Crni says, the 1986 ban will pretty much guarantee that full auto weapons will eventually vanish since there is so little of them in the first place and no new ones can be purchased.