The NRA claims that widespread gun ownership is not a substantial risk to people generally.
If this is so, there's a way to structure the law based on that "truth" and to resolve the political standoff over universal background checks.
Make background checks mandatory by federal law in all cases. But, like the "mandate" in Obamacare, there is no enforcement mechanism. That is, you are instructed to get a background check even when transferring your gun to family or friends but if you think it's a safe transfer, you can ignore the requirement, no harm and no foul.
However, if the transferee incurs criminal liability say, by a robbery.
Or if the transferee incurs civil liability, say, by firing into the air and shooting someone by accident.
Then you, who decided on your own hook that the transfer was safe, decided that you were not externalizing a threat to the commons for your own convenience....you have joint and several liability for the results of your error.
What could possibly go wrong?