Two points ahead of St Johnstone in sixth position, they will secure a top-six finish if they win at St Mirren tomorrow then at home to Kilmarnock next weekend. Even if they go no higher after the split, given the failings which went before, that will be success of a sort.
By the same token, missing out on a place in the upper half of the SPL would be a serious disappointment. In fact, for a team of Hearts' resources and ambitions, it has to be classed as failure.
"Of course it is," Jefferies said yesterday. "If Hearts set out at the start of the season they would have a target to be in a certain place, and if they don't make it then of course they've failed."
St Johnstone's next game is against Dundee United on Monday, then their last match before the split is at Pittodrie on the following Sunday. They could therefore go into that final pre-split match knowing what result would take them above Hearts, but Jefferies is not even interested in thinking about whether that gives the Perth side an advantage.
"It doesn't matter, because that's the way it is. It's in our hands – that's the most important thing. If we win our two games St Johnstone can win their two games and do nothing about it.
"The most important thing for us is we need to realise the situation, step up to the plate and make sure we do it. It won't be easy, because there is never an easy game in the Premier League, especially against two teams who will be fighting relegation.
"But St Johnstone have got a team fighting for third place to play, and Aberdeen are trying to get wins for their own cause. We've just got to make sure we look after ourselves.
"St Johnstone have done fantastically well this season. Sometimes you find that teams who come up first time tend to be an unknown quantity and go and surprise some people. They've been terrific. But we know it's in our own hands and that's the most important thing. For our own personal pride, a club like Hearts should be in the top six."
An extensive injury list has forced Jefferies to field several players out of position and prevented him from coming to a settled view on what his first-choice starting line-up is. Those problems have continued this week, with Ryan Stevenson and Gordon Smith having picked up knocks which threaten their involvement in the game in Paisley. Andrew Driver and Jason Thomson are also doubtful, and Janos Balogh, Marian Kello, Jose Goncalves, Dawid Kucharski and Michael Stewart are all still out.
"I still believe we would have been there weeks ago if we hadn't had the number of injuries we've had," Jefferies continued. "It's been one of those seasons where it's not just been two or three that's been out, it's been quite a number. We have got one or two injuries, but the team is strong enough to go there in the two games and get a result. It's in their hands: they've got to take that on board. There are two games to go and we could still lose out, but it is in our own hands and we have to go out and try and win these two games. You've got to treat it as if St Johnstone are picking up two wins, and if they pick up two wins and we pick up two wins we go."
With fourth-placed Hibs going through a lengthy bad spell, and Motherwell being only eight points ahead of Hearts in fifth, there is still a possibility that Jefferies' team could make a late push for a European place. It is a possibility, however, that is of no interest to the manager at present.
"Just let's concentrate on the two games and get in there," he said. "That's the most important thing. There's no point in talking about Europe if you don't make it. It's hypothetical.
"If we get in the top six, then we'll look above and see if we can catch anybody in those five games, whether it's the next place up or the one above that."