I think mandatory background checks on all sales is probably inevitable and while inconvenient I don't think it would be the worst thing.
Does it stop illicit gun sales? Would it have helped in the Lanza case? No, but it would at least be a bigger hurdle to keep felons and crazies away from stuff they shouldn't legally have.
I wouldn't oppose the NRA if they took the lead on that one.
Mandatory reporting requirements of stolen guns might also be something to look at because "I didn't know my guns were stolen" seems to be a get out of jail free card for straw purchasers but it would have to be written very carefully to not penalize legitimate theft victims. This one could easily head down a slippery slope.
If the NRA blows it this time I'll never send them another penny.