"Keeping records" of background checks would eventually provide a database of every person who has purchased a firearm since the law passed.
This is a de facto registry of firearm owners, only excluding those who bought no new firearms.
In the event that someone gets a bill (or amendment to another bill) through requiring private sales to go through a dealer and be subject to NICS clearance, within a generation, virtually every legally transferred (owned) firearm would be in the registry, and a very high fraction of legal firearm owners.
The enemies of this Republic have been patient when impatience would not work, and this would lay all the necessary groundwork for seizure of firearms in the future, much as registration under the Weimar Republic laid the groundwork for the seizure of firearms by the Nazis--the records survived to be used against firearm owners.
With other developments in this administration, I would never trust the Government with such a database, not now, nor in the future. Not ever.
We have seen how well-intentioned programs have been sold to the American People under one guise or another, and then used to harm our Country, our culture, and our society.
Judge this not by the good it might do in the right hands, but the harm it will do in the wrong ones.
I'm not. I believe in 'trust but verify' though not 'knee jerk before researching.'
"...and improving enforcement of existing laws regarding state information-sharing for the background check database..."
One of the problems everyone has acknowledged is that states have not been turning info on convicted felons and those adjudicated mentally incompetent over to the Feds to be put into the NICS database. Another is that some states (CO for instance) do their own background check with their own database thus missing info from the rest of the nation and wasting money in the duplicate effort. I see nothing in the statement above about Grassley's bill to indicate anything other than solving those problems. The words "enforcing existing laws" are at least some indication that the bill is not intended to expand the parameters of 'background checks.'
Beyond that everyone seems to be missing the political meaning of introducing a competing bill. It's a common method used to kill the first bill with no intention of passing the latter one. Something that's beyond the thinking of the would-be president.