I can't answer definitively, but my sense is just that your background check would be denied when you attempted to make the purchase, and the purchase simply wouldn't go through.
I've been at the counter in a gun store when a customer failed a background check. The gun store owner said, "sorry, man." The customer got pissed --"there's been a mistake!/what is the country coming to?/this is bullshit!"-- and eventually stomped out of the store. Not a big deal, really. That was probably 15 years ago, but it still stands that gun store workers aren't cops; they aren't going to arrest you. They probably aren't even going to call the cops unless you're stupid and get threatening. The system is glitchy, and the gun store owners probably sympathize more with you than with the Feds anyway.
EDIT: I am in WA, USA, where until recently we have had ridiculously relaxed gun laws. I used to joke that my concealed pistol license (CPL) came in a box of Crackerjacks --and once I had my CPL, I no longer had any waiting period or background check, the theory being that if I was safe to carry a concealed pistol, I was safe to buy a pistol. I think that privilege of the CPL has been downgraded, but I haven't bought a gun in a while so I don't know for sure. The point being --and as Retched's post makes clear-- the laws and purchase-permit requirements vary from state to state.