Already if you want to buy a weapon in a "private" sale via internet you have a local FFL send a copy of their license to the seller or their local FFL. The gun gets sent to your local FFL. You go in and pay a fee. Your FFL calls in the background check. You walk out with the weapon. It is actually, not optional for internet sales.
They are just trying to encourage willing participation amongst private buyers and sellers (non-dealers) so they are used to it and won't push back when they make it mandatory.
How will they ever enforce it?
If the law goes into effect on say...6/15/13, and you sell a gun privately after that date that you had purchased prior to 6/15/13 all you have to do is say you sold it prior to the law going into effect.
Currently you could do that with over 300 million firearms and there is no way to prove you sold it after 6/15/13.