Indeed, it has probably been the tone-deafness and intransigence of that group (both “Everytown” and “Moms” are names for “Astroturf” organizations supported by New York City billionaire Michael Bloomberg) that have stood in the way of a background bill passing out of the legislature.
The out of state lobbyists and their supporters, largely tone-deaf to gun culture in New Mexico, have attempted to lard up a background check bill with all sorts of meaningless, unenforceable, and downright offensive language regarding temporary transfers, person to person sales, and defined felony level offenses for simply transferring a gun to someone you know and trust. Thus, they have succeeded not only in alienating gun owners (a majority of whom may indeed support a rationally written background check bill) but legislative Democrats, who have to answer to voters rather than to Mr. Bloomberg.
So my suggestion? If you really want to see a background check bill passed in New Mexico, do some research into what actually works rather than what you are spoon fed, listen to true grassroots folks rather than out of state lobbyists who see every gun owner as either a pathogen or a potential criminal, and sit down with some gun folks and talk to someone outside your own bubble. It’s probably that simple.