Yes, the parts are available, but the costs are relatively undesirable. Geoff is referring to the NFA registry of full auto guns and sears, but that is a very expensive route.
But don't fret, I believe you can still legally make that machine gun you want.
The only other route would be to become a class 3 manufacturer licensee. That route is also spendy, but IIRC, you'd be able to build/convert rifles, pistols, etc. at will. However, this isn't a license the ATF will simply hand you, just because you want to play with full auto. You'd have to be in a serious business venture to acquire the 07/02 FFL, be able to pass the investigation the ATF would do, and be willing to spend all that cash. You'd likely spend just as much as the cheapest FA M16 around, but hey, you'd now be in the firearms business! You could build machine guns, convert semi-autos, and do a mag-dump every afternoon just for the heck of it! Well... I guess for the profit in it actually. The MGs you build could only be sold to law enforcement or possibly military, but could never enter the private market because, like mentioned, that registry is closed.
I think you get the point though.