Just tell the gun lobby that if any of the Gun Shops keep an online database of their customers that's subject to the law. No need to worry about a national gun registry, the GOV gets it for free. Get the NRA involved and ALL OF CONGRESS will run screaming about how this goes against the 2nd Amendment.
This actually would work. I think the general public either (a) doesn't know about this law at all or (b) doesn't think it will interfere with their daily activities. Getting other big organizations who value privacy would help solve both problems. I think that anyone who begins to understand the law will be opposed to it.