How does that stack up against "the right of the people to keep and bear arms, shall not be infringed"?
The constitution is not something that can be changed by reinterpretation or by mere legislation. It must be amended to change it.
While the types of arms we are talking about may not have existed at the time the 2nd amendment was ratified, the constitution and it's meaning have not changed. The right to keep and bear arms shall not be infringed.
The only reason I would desire an automatic weapon is as a curio. I might be interested in owning a weapon capable of short bursts (3 rounds), but a fully automatic weapon just doesn't seem very effective to me, unless it's mounted on a tripod or something else to make the recoil manageable.
A hand held fully auto weapon is just a way to waste ammo.
However, that doesn't mean I think the government has the authority to ban them without first amending the constitution.