Put plainly, the New York Times is the New York Times. Swing voters in Middle America aren't its subscribers, and the swing voters in Congress don't have to appeal to voters who care much about what the New York Times thinks. In fact, you could make a pretty convincing case that this would have the opposite of the intended effect by overreaching on something most Americans simply don't think will do much to prevent mass shootings.
... accused the "mainstream media" (of which the Times is a flagship member) of advancing a liberal agenda. What they often fail to recognize -- or deliberately ignore -- is the separation of news and opinion. ... Most of the time, their complaints are unfounded or greatly exaggerated.
In this case, however, the Times has (at least temporarily) knocked down a wall by placing an editorial in a spot normally reserved for news. That does not mean the paper's political reporters will suddenly abandon all sense of fairness as they cover candidates who staunchly back gun rights. But it does give those candidates new cause for suspicion -- a cause they will almost certainly exploit on the campaign trail.