I believe the specific case that Biden referred to, and that touched this all off, was that a company put together kits that had everything needed to build a complete firearm with the lower being an 80% lower. It included all the interior parts for the lower, the barrel, slide, etc. I have a vague memory of ATF raiding a store front doing this and selling the kits through the internet. I do not think they were breaking the law but they sure pushed the limits of it.
I am sure that the only way the ATF can do anything is by defining a ghost gun as a kit that can be used to assemble a complete firearm that has a partially milled frame. If they do anything else, they will kill the used and accessory parts market (which I doubt would bother them other than their losing the cases in court). If they try to define an 80% lower, people will go one step further from complete and sell 75% frames, ad infinitum. This can only result in defining blocks of metal as firearms and that won't fly either.
I predict that some definition of a kit to make a firearm will be created and then banned (well, maybe just defined as a firearm and the dealer would have to be an FFL and run a background check, which implies a serial number on the frame). Even this is pushing the limit of the law, but would be harder to find someone to fight it in court.