Yeah. If anything, this proposal would make Americans care even less about mass shootings. The families were compensated, so at leas there’s that! We keep hearing, after these types of shootings, that we need to “do something”. Well, this is “something”. It makes no sense to think this will make Americans care more.
So what’ you’re saying is we’re going to pay the victims of mass shootings, and we’re going to make [del]the Mexicans[/del] the vets pay for it! 
One hopes this was said in jest.
The OP’s proposal already suffered by a needless invoking of veterans’ benefits, which have nothing to do with compensating a class of crime victims. While this example may have meant no such intent, such a comparison carries an odor of resentment and hostility toward attention/honor given to present or former members of the armed forces, a politically counterproductive and otherwise dubious attitude seen all too often in discussions on this board.
You may sense that odour but the OP is former Navy and iirc, works for them still as a civilian. From the OP “and I say that as a veteran myself”. Is your indignation based on your own service?
I think it’s a mistake to assume that the public’s resistance to gun control proposals means that Americans don’t care (much?) about mass shootings.
Yeah, that was not worded well. What I meant to say was make Americans inclined to do even less about changing gun control laws in reaction to mass shootings. We talk like we want to do something, but we rarely do. This would lower the impetus to act.
Functionally, it is the same thing. Like an alcoholic who “knows he has a problem” but the solution never seems to involve stopping drinking.
Well, however much they care about mass shootings, they care about their guns more.
“They” being the cohort of Americans who are resisting gun control proposals, a fraction of “the public” overall. I daresay the largest relevant cohort is the ~50% of the American electorate who don’t care enough to bother voting either way.