My assertion is the the proposed regulations do not state the mechanism by which the regulation will affect gun deaths to any appreciable degree and until that is clear, I will oppose them. If we know the population that is the source of gun deaths, then show me how your proposed regulation will specifically affect them.

Certainly a fair point. And especially when it comes to mass shootings, there is often a disconnect between what is proposed for 'commonsense gun regulations' and the specific problem of mass shootings (such as the gun show loophole, when mass shooting weapons are not identified to be more commonly bought at gun shows).

Generally, the argument comes down to ubiquity. Those skeptical of gun control tend to describe gun usage in terms of planned crimes: criminals will find ways to get guns, no matter what the rules are. Someone who intends to rob a convenience store using a gun is going to get a gun, which might result in a clerk getting shot. If that's what you think of when you think of gun use, then it's easy to see why you can't see the mechanism for reducing those deaths.

But many (if not most) instances of gun use are spontaneous, not planned. For example, the recent shooting death of a seven-yr-old here in Florida stemmed from a fight over a jet ski:

cbsnews.com - Boy shot dead tampa florida jet ski dispute grandfather wounded

...and it happened not because the shooter planned to kill someone that day, but because he happened to have a gun handy at the time when he lost his temper. If it was illegal to carry your gun around with you all the time, he might have chosen to leave his gun at home. The conflict might have still escalated into violence, but it would be far less likely to result in a fatality - and not a bystander fatality. That's the reasoning behind "cooling off periods" and barring Saturday night specials as well - people end up using guns spontaneously in the moment they're most angry if those guns are easy to grab at that moment, but if they're not at hand they have a chance to exercise better judgment. And of course, the same reasoning applies to suicides. But that disappears if most people already have a gun lying around that they bought a while back.

So the idea is that if you have simply have fewer guns in fewer places, you'll have fewer of these non-premeditated gun deaths. Make guns rarer, more difficult to obtain, and not always at hand....and you'll end up with fewer gun deaths. That was the experience in Australia after their gun buyback - you saw dramatic reductions in gun deaths in the scenarios where gun usage was most likely to be opportunistic rather than pre-planned, such as suicides and spousal murder:

vox.com - Australia buyback

Whether you can extrapolate the effects of a major change in gun access (like Australia's) to the relatively minor inconveniences that "common sense gun laws" might impost is uncertain. But that's the idea.