Mandated Gun Ownership

How would requiring the ownership of a gun be different from requiring the purchase of healthcare?  Its just a tax if you don't buy one, so why not the other?

The small town of Nelson, Georgia, (pop: 1,300) passed an ordinance in April requiring the head of each household to own a firearm (with exceptions for convicted felons, those not capable of owning a gun, and anyone who conscientiously objected. Despite the exceptions, and that the town’s police chief (and only cop) said he had no intention of enforcing the ordinance, the Brady Center for Gun Violence (an anti-gun more than an anti-violence group) is suing the city over what it calls an “unconstitutional” law.

-reason

from the comments:

The GOP should quietly threaten to pass a mandatory gun law if the Democrats don't repeal ObamaCarousel. Sure, deny it publicly, but make it clear that they'll do it as soon as they have the votes.

What part of the constitution grants the government the power to enact such a regulation?

The same part that says that the government can compel you to purchase a product from a third party.

In my book, the people in a state or a municipality can pass their own local constitution which grants their local government powers which do not conflict with the Federal constitution. Any authority the people have not granted to the local government in such way, the local government should not have.

If government can force you to have fire extinguishers, smoke detectors, and low flow toilets and showerheads why can't they force you to own a firearm?

According to the FedGov, the National Militia includes every able-bodied man between specific ages. Requiring that everyone own a firearm supports this definition of "militia" in a very practical way. Too bad towns are having to do the work that the FedGov just isn't willing to do.

The government can't require people to do something unless there's some plausible argument that it serves a legitimate government objective, Perry said. While deterring crime could be considered a legitimate objective, it would be hard for the city to prove the ordinance accomplishes that goal, he said.

Step 1. Fight this lawsuit and ultimately lose because "it's hard for the city to prove the ordinance accomplishes that goal."

Step 2. Sue Chicago and demand they prove that their "common sense gun control" laws accomplish the goal of reducing gun violence.

Step 3. Sue D.C. and demand they prove that their "common sense gun control" laws accomplish the goal of reducing gun violence.

Rinse-repeat.

Just which Constitutional right does this law violate, again?

Note that this has nothing to do with any of purportedly limited grants of power to the feds, so the Commerce Clause and all that are irrelevant. If this is unconstitutional, it can only be because it violates a Constitutional right. So, which one?

In light of the Obamacare decision, which one indeed?  And why not try it?