Wouldn't a good first step be to enable Brady background checks on private sales? I mean i think this could be done through executive order and could absolutely be done through congressional regulatory change.

Second, why would the "gun lobby" that is always claimed to be driven by gun manufacturers want private sales to have less regulation than every one of their sales require?

No, there will never be federally mandated background checks on sales between two people living in the same state which neither are in the business of selling firearms. Her time would be much better spent lobbying states where it is possible. Not that many states are likely to require them without the feds first making use of NICS possible for private transfers...

After dozens of massacres, you actually had conservatives voting against their party platform to save lives, and since the vote there have been no more massacres and fewer gun deaths. We can do it here too. And note: they still allow people to have guns. They just have stronger regulations. We need to stop equating more regulation with "Obama wants to take your gun". One day I think we will.

Daily Show did a nice piece on this
http://www.amazingvideos.me/listing/the-daily-show-john-oliver-investigates-gun-control-in-australia--part-1-127