I think Trump will just introduce a "poison pill":
Put the "instant check" system on line, where somebody can enter a drivers license (or other state ID#) and name into a web page, and get back whether the person is ineligible to own a firearm, along with a confirmation number to show that the name had been checked. Doing this check would insulate private sellers' from any liability for selling to an ineligible person.
BUT, no firearm serial number would be entered, so it could not be used as the basis for a registration database.
AND the web service would be open to ALL, not just firearm sellers. Women could use it to check out new boyfriends. Employers could use it for prospective hires. Apartment owners for tenants. It would get so much use that it would be utterly worthless for gathering firearm data.
The Dems would shoot it down, and Trump would walk away saying "See? They are not serious about stopping sales to bad people!"
But men would be forbidden to use it to check out new girlfriends. That would be sexist. Women are always good
only men are suspect and need to be "checked out".
I certainly hope that he will do something like that!
Poison pill is exactly the tactic he wants to use!