Universal background checks can not reduce murder.
The fallacy with so called "universal" (or otherwise) back ground checks is fundamental.
They absolutely positively do not reduce murder because they can't.
Sure it sounds all nice and warm and fuzzy with reasonableness to most folks.... But consider the following:
1) Nobody needs a gun to murder. Criminals have practically an infinite number of tools with which to do that with. They are often not even the most effective for murder. They are simply popular to use as a tool because of their convenience. But convenience is ONLY critically important for defensive purposes not for attacking others.
2) Practically nobody who has been "stopped" by background checks serves prison time. Even though it is a felony to even fill out the form if you're a prohibited person.
3) The overwhelmingly vast majority of people who have been "stopped" by back ground checks are simply folks who have similar information to prohibited people. I'm sure many were not in dire need of a firearm to protect themselves but certainly some significant percentage did need one for protection.
4) Most mental health records are not included (mental health is obviously the heart of the mass killer issue not so much common criminals) and when you start to research you see that it is quixotic to even try to fight through the privacy/civil liberty issues that prevent the reporting of many/most mental health issues. And nobody needs a gun to murder.
5) It is already illegal to sell to a prohibited person so the majority of folks who do, would not be running a background check regardless of the law. When you are bartering with a stolen gun for some meth, it is terribly unlikely you will be going to get a background check done. And nobody needs a gun to murder with.
6) Criminals and crazy folks can and often do simply steal guns (see Adam Lanza and Newtown) from people who are not prohibited. The most universalist super investigative inclusive background would still fail to stop somebody determined to get a gun to murder with... And more importantly nobody needs a gun to murder with.
7) See #1 nobody needs a gun to commit murder, mass or otherwise.
8) The justice department has already stated that a universal background check will never be effective with out a national registration. (In fact it will never be effective at reducing murder period even with registration but I suppose its possible to be effective at reducing gun use in general, but not murder). Registration as always always always lead to confiscation in every country that has had it. Even here in the US.
In summary the system is not just broken and practically unfixable (without trampling all over civil liberties) but even if it wasn't broken it still could not prevent any murder because fundamentally its not possible to reduce murder by restricting access to guns. Primarily because nobody needs a gun to murder. Back ground checks can and do ONLY negatively effect the ability of people to defend them selves.