From Reason.com:

On the face of it, there is no downside to broadening the background check requirement, and it might stop would-be mass shooters and other violent criminals from arming themselves. Advocates portray a system of “universal background checks” as the epitome of “commonsense, bipartisan gun violence prevention legislation,” the sort of policy that unites reasonable people across the political spectrum. It seems you’d have to be a crazy extremist to oppose the idea. Yet if you dig into the details, you will find sound reasons to be skeptical.