I haven't read all the replies, but I'm not opposed to background checks for private party sales... PROVIDED the following criteria are met:
NO registration of firearms or firearm transactions. Congress has repeatedly prohibited it, because registration is the first step toward confiscations. Ask our friends in the UK and California.
NO need for an FFL to get involved. Private citizens should have access to the toll free NICS number.
A limit on the amount of time that records need to be kept. Five years to seven years sounds like plenty of time to me.
NO charge. We pay enough for Government services already. Licensed dealers don't pay a fee for the NICS check, American citizens shouldn't either.
A waiver for those who are exempt from a NICS check when buying from a dealer - CPL holders and those with a purchase permit.
I seriously doubt it would have any impact on crime, but I'd go along with it. Unfortunately, I doubt the anti-gun crowd would ever agree to terms like these. Their goal is not to insure that buyers are qualified, they're only looking to make transactions more difficult and create a database.