His chances of steering the faltering European champions into the knockout stages of the competition are slim as they not only have to beat Denmark's Nordsjaelland but also need Juventus to slip up against group leaders Shakhtar Donetsk.
The Ukrainian side have already qualified while the Italians, two points ahead of Chelsea, know a draw will suffice to see them through to the last 16.
Such is Benitez's low standing with Chelsea fans after he was parachuted in last month to replace the popular Roberto Di Matteo, that achieving the feat of hauling the club away from the European rocks may do little to appease Chelsea's bloodthirsty faithful.
Having booed the Spaniard before his first game in charge, his stock fell to a new low after Saturday's 3-1 defeat by West Ham United which left him without a victory in his opening three matches at the club.
"We have to improve on the pitch in order for the fans to be happy," Benitez told the club website.
"We have experienced players who have played at this level for a long time. You can see how they train and it's clear they want to improve."
Benitez's excellent record in the Champions League could have acted as a comfort to Chelsea fans had his success not arrived principally at their expense.
At Liverpool he reached two Champions League finals, winning one, with a squad of players that was modest in comparison to Chelsea's at the time, a fact that made two semi-final triumphs over the West Londoners a bitter pill to swallow for the fans he is now trying to win over.
Should results go against Chelsea they will become the first holders of the trophy to exit the competition in the group stage, and it would be the first time they have failed to qualify for the last 16 in any of the 10 previous campaigns.
Benitez is by title only Chelsea's interim manager, but British media has already started to speculate that his spell in charge will be shorter-lived than anyone could have thought.
The Danish champions should provide Benitez with his first victory as Chelsea manager. They have not won a game and have only a solitary point after their five matches in the competition.
Nordsjaelland, beaten 4-0 at home by Chelsea in October, sit second in the Danish championship, nine points behind leaders FC Copenhagen.
Chelsea: 1-Petr Cech; 28-Cesar Azpilicueta, 2-Branislav Ivanovic, 24-Gary Cahill, 3-Ashley Cole; 12-John Obi Mikel, 7-Ramires; 10-Juan Mata, 17-Eden Hazard, 11-Oscar; 9-Fernando Torres.
Nordsjaelland: 1-Jesper Hansen, 18-Michael Parkhurst, 2-Jores Okore, 21-Ivan Runje, 8-Patrik Mtiliga; 6-Enoch Adu, 7-Nicolai Stokholm; 20-Kasper Lorentzen, 17-Soren Christensen, 15-Joshua John; 11-Morten Nordstrand
Referee: Bas Nijhuis (Netherlands).
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