They can go as far as the WWE creative team and Vince McMahon want them to go. Right now though there are a couple of major hurdles to get over.
First of all Sheamus is holding a guaranteed contract for a shot at the world title. The have to get the suitcase off him somehow, or this team will never go anywhere, or be believed to be an actual team. Like someone else said, if Sheamus get's his opportunity to go after the title, he's gone.
Now in saying that, they've done nothing to build Sheamus up since he won the damm thing. Most of his matches have been tag affairs anyway, and once, only once he tried halfheartedly to cash in. He carries the briefcase like it's a prop now, and I don't think he or the WWE is serious about a Sheamus title run. It would come out of nowhere and go exactly the same place, nowhere.
Barrett has been very lucky and unlucky at the same time. Just when he got on a roll he got injured, twice. He's sort of another Sheamus, in that they give him the KOTR, which in this day and age means absolutely nothing.
So you have two guys, one with a crown and one with a briefcase as a tag team. Get rid of the crown, and the case and you might have a good team here. They are both brawlers, suit each others styles well, and could be formidable when they get going.
Would love to see them against Harper and Rowan, or Harper and Strowman. That would be one hell of a match. They won't be as entertaining as New Day, but then no one is, so it's not really a slight against them.