First is the idea of registration; lots of people are against it, for various reasons.
Second is the definition of "transfer" and the potential for confusion and abuse by the authorities. For example, can I loan a friend that I know can legally buy guns a gun of mine for a weekend hunting trip? Do I need to do a background check for that? How long in terms of time and/or distance could I loan a friend a gun? If my sister gets beaten by her husband and goes into hiding, can I loan her a gun?
Third is the idea of effectiveness. Does it work? What is the primary source of guns for career criminals? How much of a deterrent is not being able to buy a gun to a career criminal or a determined purchaser? My state currently has some of the strictest gun laws in the country, yet there are still plenty of dead bodies with bullet holes in them.
Fourth, what about false positives?
Fifth, what about under-funding the background check system with the intention of denying people the ability to purchase guns? A parallel example would be Scott Walker's Wisconsin requiring photo ID to vote, then closing down lots of DMV offices in "certain" areas to make it very hard for "certain" people to vote.
The concept isn't horrible or evil, but the execution is up for discussion.