From an enformcement point of view, any universal background check law requires a record of transfers in order to determine when a specific firearm left "the system" without passing through a background check so the last legal purchaser of the firearm can be tracked down and charged with failure to run a background check on the person they sold it to. Such a record becomes a defacto gun registry via a legally enforcible record of the last legal owner of any firearm transfered after the implimentation date.
Once the firearms transfer registry exists, it is impossible to remove it from the hands of the government. Passing a universal background check requirement gives every future government immediate access to the identity of every legal, law abiding gun owner. If any future government decides that it is no longer in the government's best intrest for civilians to be armed, such a registry provides them immediate access any law abiding citizen who has purchased a firearm since the passage of the universal background check, allowing government agencies to visit said people. Any person who can not produce a firearm which was last legally transfered to them could then be arrested for suspician of violating universal background checks. Much as was done by the elected government of Germand in 1938 using a 1919 firearms transfer registry to identify potential gun owners.
In a much less sinister possible future, a criminal trafficking organization could obtain a collection of "clean" identities to make gun purchases, purchase as many guns on each identity as will not raise suspicion, then illegally transfer said firearms to the black-market without proper background checks. When such firearms begin to be recovered by law enforcement at crime scenes, the person who's identity was fraudulently used to purchase those firearms will be contacted by police and investigated for possible gun trafficking.
The result will be increased risk and hassel for law abiding citizens, increased identity fraud that will be nearly impossible for an individual to detect until they become the subject of an investigation (will I be able to contact NICS and find out how many NICs checks have been run on my ID?) with zero improvement to public safety.
If you're having a discussion with someone about this, here's some facts to remind them of:
1) The Shooters in Columbine obtained all of their firearms illegally
2) The shooters at Virginia Tech and Aurora, CO obtained their firearms with a valid NICS check
3) The shooter at Newtown, CT was denigned by a NICS check, but all evidence indicates his mother purchased firearms FOR HIM anyway.
"Universal Background Checks" would have had no impact on any of these trageties as all of them either passed the system or illegally circumvented it under current law.