Judging by the manner of Wednesday's 2-1 defeat at home to strugglers Guingamp in the French League Cup quarterfinals, he will need to be wise and ruthless in his decision-making over the next few weeks.
Although it was only PSG's second defeat of the season it was as humiliating as it was unexpected and, if he was watching on TV in chilly northwest England, Solskjaer may well have gone to sleep with a smile on his face.
Momentum is shifting back in United's favor following a dismal start to the season under then-coach Jose Mourinho, while PSG is coming under some pressure after making a blistering start to its French league campaign.
Goals were flying in from everywhere, Kylian Mbappe and Neymar were scoring for fun, and Tuchel received high praise for man-managing his stars with a feel-good approach rather than a firmer and unpopular one employed by his predecessor Unai Emery.
Tuchel's stock among fans and players,grew further after his side beat Liverpool 2-1 in the Champions League, effectively preventing the possibility of a group-stage exit . The euphoria faded when PSG drew back-to-back league games away to Bordeaux and Strasbourg. Neither of those sides has stars, but their coaches frustrated PSG by playing an intensive pressing game depriving them of space and forcing them into errors.
It's a simple but effective formula when done right, as Guingamp also showed and Solskjaer will doubtless have noted. The sloppy defeat to Guingamp, with three penalties conceded in the second half, raised alarming questions about a lack of concentration.
With insufficient protection from midfield, PSG's defense was far too easily breached, prompting rash mistakes from defenders inside the penalty area. Thilo Kehrer, a promising young German defender, has given away four of the 10 penalties PSG has conceded this season.
There were no excuses at either end as a glittering forward line comprising of Mbappe, Neymar and Angel Di Maria — costing a combined 465 million euros in transfer fees ($535 million) — fluffed chances against the side last in the first division.
Tuchel put it down to complacency, a criticism often labeled at PSG's players in the past. "We were over-confident for nearly the whole game ... we thought nothing could happen to us and that we'd win, we'll score and then it's over," he said. "It's our challenge to accept and to improve. You learn a lot from a defeat, no one likes it, but it's necessary in sport to grow."
The accepted reasoning is that PSG's lopsided domestic dominance leads to such over-confidence, which is then punished by equally big — or bigger clubs — in the Champions League. Real Madrid knocked out PSG last season, Barcelona the season before, and equally ambitious nouveau-riche club Manchester City did so in 2016.
But it is beginning to sound more like an excuse and has to stop immediately. If PSG wants to be acknowledged as a leading club, rather than an emerging one, it has to go far in Europe because, since cash-rich Qatari investors QSI took over in 2011, PSG has never reached the semifinals.
Reaching the semis seems like the minimum Tuchel needs to prove he's the right person to take the club forward. This season is therefore shaping up as make-or-break for PSG and for Tuchel given what happened to his predecessors.
After two years in charge, Emery's contract was not renewed despite leading PSG to an emphatic domestic treble last season. Laurent Blanc was given a new contract in early 2016 and then abruptly sacked a few months later to make may for Emery.
Like Emery, Blanc won the domestic treble but ultimately paid the price for his side's shortcomings in Europe. To exceed them, Tuchel has to deliver in Europe's biggest club competition.
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Jerome Pugmire is at www.twitter.com/jeromepugmire