You don't have the right to own a gun "if you pass a background check".
Also OP, what about guns not bought from a dealer? Do you want that big background check for all sales and transfers, even between family members?
Once you give the Govt the power to regulate gun sales via background checks they are going to go bananas with it. Right now you can't buy a gun with a restraining order... anyone who has been divorced (or in my case, worked for a family court lawyer) knows that restraining orders fly like the birds and that it's almost just a formality in many cases. That should NOT keep you from buying a gun.
The Govt could add to the list of disqualifiers as much as it wanted... maybe no service men who have seeked mental health care can buy a gun.. maybe no registered libertarians may buy a gun.. maybe no one who is late on their taxes, or who has a speeding ticket, or who already owns "too many" guns may buy a gun...
Also, what about the guns you ALREADY own? To implement this background check would be useless because every gun (100 million+?) in private hands has been bought or transfered without it. Would every gun owner in America be subject to it? What would be the out of pocket cost? Maybe like an NFA weapon there will be a tax on this backgrounc check... afterall that was the purpose of the $200 NFA tax, to keep it away from the riffraff.
Even if EVERY gun were trransfered with your imaginary background check, mass murders wouldn't stop. There is already a black market for guns, you can believe it would only increase. Also, you can still buy fertilizer and racing fuel and rent dump trucks, so you can level a building full of people without a background check.
Or I could just manufactor my own full auto M16 and go on a killing spree anyway. I could email you the 3D blueprint for a lower receiver, or an entire handgun, and with a poly printer you can press "print file" and you will have a firearm coming out of your printer. No background check needed for printers or email addresses.
So what would be the result of this march to folly? Great cost, gross over regulation, zero positive impact, and by then the gun grabbers will only be stronger, and they will be asking for more more more.
Don't be deceived, they want every single firearm off the street. You can hunt with a bow and protect your home with a baseball bat in their opinion. Meeting them halfway, or even budging .001mm is only helping their cause and hurting yours... it is moving toward total disarmament.
Oh yeah, and "shall not be infringed" is pretty specific.
Still confused?