As long as there is not registration involved I can't really get excited about background checks. I don't want to sell to a felon at any rate. Background checks for in family transfers would be the height of stupidity.
What I do have concerns over is the taxing of a right - if its ok to put a tax on bearing arms, then its ok to demand an ID that might cost some money to get to avoid voter fraud.
However, the thing that I see that most violates our rights of all proposals is the bans etc that try to restrict the arms most pertinent to the intent of the 2nd Amendment, from possession by the citizens that were meant to be armed as a deterrent to abuse by their own govenrment.