Not sure what action you mean, but if they come out and admit they blew the call and cost the Saints the game, they could face litigation of some sort from people that lost insanely large sums of money as a result.
If they come out and decide to use that rule and replay the game from that point, Goodell would be shark food in no time. Vegas has already paid the bets they owed which they can’t get back. But they could be forced to pay out millions/billions more if the Saints were to cause the game to be a push or if the Saints ended up covering the spread.
I think they are just trying to let everything settle down before they admit a mistake and announce it in a way that places zero liability on them.