Against New Zealand in Brisbane last month in Mckenzie’s last match in charge, they were in front five minutes from the end before going down 29-28 to a late try.
In Mendoza a couple of weeks earlier, they blew an early 14-0 lead to hand Argentina their maiden Rugby Championship win. That followed a 28-10 loss to South Africa in Cape Town after they conceded three tries in the last 10 minutes.
The New South Wales Waratahs developed the knack of just getting over the finish line under Cheika this season, most notably when Bernard Foley slotted a decisive late penalty to give them a first Super Rugby title in May.
Flyhalf Foley was also Australia’s match-winner at the Millennium Stadium on Saturday, a drop goal and penalty in the last eight minutes handing the Wallabies a 10th straight win over the Welsh and a first victory away from home this year.
The 25-year-old could easily have been the villain, though, after kicking away possession in the dying seconds to allow the Welsh one last charge at the tiring Wallabies defence.
In some ways Foley’s performance summed up that of his team, good enough for victory over one of Australia’s group rivals at next year’s World Cup but certainly not perfect.
“There’s plenty to improve on, we’re not claiming that we had a cracker,” Cheika told reporters in Cardiff.
“It’s been two weeks of getting our heads together and playing a new system. The guys getting into that, defensively as well, not just attack.”
If, over the next 10 months, Cheika can fix the problems at scrum time which led to a penalty try for the Welsh just after the hour mark, he really will be able to claim to be a miracle worker.
What will undoubtedly improve under Cheika, though, is the physicality of his forwards in the early exchanges which are so important in establishing a foothold in a match, especially against northern hemisphere teams.
Injuries have not helped — Australia are down to effectively their fourth, fifth and ninth-choice hookers on this tour — but it is an area which will be sorely tested by France, Ireland and England over the next three weekends.
(Editing by Peter Rutherford)