Once you agree that the second amendment can be limited in its application to convicted felons, which many here agree with, I think you almost have to allow for a way to verify the eligibility of a purchaser. That's what the NICS system does, but it isn't perfect. A lot of Nebraskans prefer getting the purchase permit once every few years as opposed to a NICS check every time you make a firearm purchase. Should it be free -- yes, if it's required. My personal preference would be to make the permit optional and keep the fee. You either go through a NICS check or present a permit. That way those who don't want the hassle of a NICS check can avoid it, but the cost doesn't fall on all the taxpayers.
As a practical matter, this isn't a hot-button issue for most gun owners in the state and would not get any traction in the unicameral. I personally don't think it's a fight the NFOA should engage in at this time. There are too many other things to go after in the legislature.