As far as I know, the NRA position on background checks has not changed. The NRA still supports checks between dealers and buyers. However, the terms, have changed to 'Universal checks" for “transfers" of all guns. In practice, it would intrude on transfers between family members. This would lead to recording the details of the gun and the names of the gun owners--thereby creating a gun registry and de facto gun registration. Therein lies the resistance. The NRA, as well as gun owners are worried about how a gun registry will be used, as historically gun registration has lead to confiscation. The oft-cited polls showing support for "Universal background checks" omit these key details, which skews the result. The issue for gun owners is not the background check--it is about registration.
For proof that registration does nothing to reduce “gun violence”, I give you Chicago.
In 2012, Chicago exceeded 500 homicides, 435 killed by guns.
Besides the exceedingly, excessive restrictions on owning a handgun in Chicago, (which requires gun registration,) Illinois is one of the few--if not only--states to require gun owners to have a Firearm Owners Identification (FOID) card. You must have this card in order to (legally) possess, buy and sell both guns and ammunition. In addition, the statute reads:
“Any person within this State who transfers or causes to be transferred any firearm shall keep a record of such transfer for a period of 10 years from the date of transfer. such record shall contain the date of the transfer; the description; serial number or other information identifying the firearm if no serial number is available; and if the transfer was completed within this State, the transferee’s Firearm Owner’s Identification Card number. On demand of a peace officer such transferor shall produce for inspection such record of transfer.”
To recap then, to possess even one bullet in Illinois, one must have a FOID card. Most of the guns could be traced to the seller--IF the transfer was done legally. I think you could confidently assume that the killers in Chicago do not have a FOID card, and did not buy their guns from a FOID card holder.
Registration will not do--and has not done--anything to stop the flow of guns to criminals.