Pretty sure the NRA does not support any gun regulation (I don't know, I'm not a member). They didn't seem to put up to much of a fuss over bump stocks, it didn't seem.
This maybe happens at the state level more often but the NFA is a good example. The line of reasoning goes "We are only banning a certain aspect of the gun, say the mag size, stock type, handle type, length of gun, etc, but you can still own the gun. So people go along with it because it doesn't seem that bad, we compromise. Then next year its something else to go after. Some tragic event happens and people say oh we need to ban some other random aspect of the gun so that they will be less dangerous. This process continues, but nothing is accomplished except making it difficult on law abiding citizens but not making anyone safer.
I personally agree with background checks, but it's just one more restriction in a sea of many actual and potentially forthcoming.