The Gorgie club racked up a sixth successive SPL victory last night, defeating Motherwell 2-1 at Fir Park to move three points behind second placed Celtic and six points adrift of leaders Rangers at the top of the table.
It is Hearts' best run since their memorable start to the 2005-06 season when they set the early pace at the SPL summit before George Burley's dismissal as manager. While they have now played a game more than both Old Firm clubs, their current form has inevitably sparked discussion of whether they can sustain a championship challenge.
"Our team is definitely growing in belief and confidence," said Jefferies, "and you are always going to be asked the question about splitting the Old Firm when you are on a run like this. But Rangers and Celtic are two big clubs and there have been clubs in third place before, like Hibs and Dundee United in recent years, who have been asked that question. It is an easy thing to say you are going to do it but it probably just riles Rangers and Celtic when you do that. It is about stepping up to the plate and doing it on the pitch that counts.
"If Rangers and Celtic slip up, as they have done in some games recently, then we have to try and cash in on it.
"I'm not saying we can split them, but I think we have a team who can push them all the way. Who would have thought at the start of the season, with the way Rangers and Celtic were both winning every week and people were talking about a record gap between the Old Firm and third place, that we would have reached a stage where we are three points behind?
• Match report: Motherwell 1 - Hearts
"It is a fantastic achievement for the players. That's eight wins out of nine now and the place is buzzing. It was bedlam in the dressing room after the game because everyone knew this was a huge result for us."
Hearts conceded their first goal in six games last night, Keith Lasley's strike equalising for Motherwell on the stroke of half-time after a Mark Reynolds own goal put the visitors in front. Kevin Kyle's 60th minute penalty, earned by the outstanding David Templeton, saw them secure a win which Jefferies regarded as the most impressive of their current run.
"It is another notch up for us from recent wins.On Saturday against Aberdeen, we cashed in against a team low on confidence, but tonight we beat a good side and showed that the players waiting for their chance can do a good job," said Jefferies.
Motherwell caretaker manager Gordon Young, who is likely to be in charge again for Saturday intriguing match at Pittodrie against an Aberdeen side now managed by Craig Brown and Archie Knox, had no real complaints about the outcome last night. "I thought we suffered from not having played for a couple of weeks," said Young. "We equalised at a great time at the end of the first half but never kicked on from that. We looked a bit leg weary and I now need to galvanise the players before the weekend."