Mauricio Pochettino's side, runners-up in the Champions League last term, have taken just one point from their opening two games in Group B and know that anything other than victory in this one would leave them facing an uphill struggle to make the knockout rounds.
It will take a long time for the wounds to heal after the mauling Tottenham received in their most recent Champions League outing, when they conceded five second-half goals en route to a 7-2 humiliation by Bayern Munich.
As if that was not bad enough, the main punishment was meted out by former Arsenal man Serge Gnabry and, while there was some truth in Pochettino's post-match comments that the final scoreline was harsh on his side, he could also have no arguments that they were emphatically second best in the end.
The result had statisticians reaching for the record books; it was the heaviest home defeat any English club had ever suffered in European competition and the first time in Tottenham's 137-year history that they had conceded seven times at home in any competition - certainly not a moment they would have wanted the Amazon cameras to capture.
Worryingly, that capitulation is not even the undisputed nadir of Tottenham's recent form - they have also been beaten on penalties by League Two Colchester United and lost 3-0 to Brighton & Hove Albion within their last five games, and the latter result was compounded by captain Hugo Lloris suffering a sickening arm injury.
The international break seemed to come at the perfect time for last season's beaten Champions League finalists, then, only for the poor form to continue on Saturday when they needed a late goal to draw 1-1 at home to Watford - a team still waiting for their first Premier League win of the season and against whom Spurs have historically had very little trouble beating.
It is now just two wins in 11 games across all competitions and none from their opening two Champions League outings, throwing away a two-goal lead against Olympiacos on matchday one before their bludgeoning by Bayern.
Indeed, despite making it all the way to the final last season Spurs have won just one of their last six matches in this competition, conceding 18 goals in that time.
On a positive note, Spurs are in a better position now than they were at the same stage of last season's group stage, when they lost their opening two games and had just one point after three before going on to progress and make it all the way to Madrid.
Tottenham's domestic form was much better then, though, and while the desire to still be in this competition after Christmas will obviously be strong, the priority at this stage is perhaps to improve on a woeful run of just 23 points from their last 21 Premier League outings.
Pochettino's side have also only won three of their last 10 matches at their new stadium - losing half of those - and know that their away record is considerably worse than even that, so an improvement in front of their own fans in needed first and foremost.
A home tie with Red Star looks eminently winnable, but then again so did Saturday's game against Watford and the visitors will arrive at the Tottenham Hotspur Stadium full of confidence following a six-match winning streak which has seen them score 21 goals.
That run includes a 3-1 triumph over Olympiacos on matchday two which puts them second in Group B, behind only a Bayern Munich team against whom they lost 3-0 away - a reasonable result with the hindsight of how Spurs fared at home to the Germans, particularly considering two of those goals came in the final 10 minutes.
Red Star did ride their luck at times in the win against Olympiacos, but they are also a team which beat eventual winners Liverpool in last season's group stages and who have once again earned their place in the competition proper from the very first round of qualifying.
However, it should also be noted that Red Star's best moments in last season's groups came at home; on the road they lost all three games and conceded 13 goals, while including qualifiers they are now nine games without an away European victory.
Nevertheless, Red Star are a side with a winning habit and capable of scoring goals, so they represent dangerous opposition for a Spurs team seemingly devoid of confidence at the moment.
Spurs Champions League form: DL
Spurs form (all competitions): LLWLLD
Red Star Champions League form: DWDDLW
Red Star form (all competitions): WWWWWW
Spurs will hand a late fitness test to playmaker Christian Eriksen, who missed the Watford match after picking up a dead leg on international duty but is expected to have recovered in time for Tuesday.
Eriksen's absence opened the door for Dele Alli to make his first Premier League start of the season, marking the occasion with a goal which also puts his name forward to retain his place in the side for this one.
Captain Lloris will not play again until next year after damaging ligaments in his elbow, while the game is also expected to come too soon for summer arrivals Giovani Lo Celso and Ryan Sessegnon, although both are now back in training after injuries.
Red Star, meanwhile, could be without Richmond Boakye due to a calf injury which has kept him out of the past two games.
Former Wolverhampton Wanderers and Huddersfield Town winger Rajiv van la Parra is pushing for a recall to the starting lineup, while other familiar names to English audiences include ex-Chelsea man Marko Marin and Jose Canas, who played alongside Tottenham's Ben Davies at Swansea City.
Tottenham possible starting lineup:
Gazzaniga; Alderweireld, Sanchez, Vertonghen; Aurier, Ndombele, Winks, Davies; Son, Eriksen; Kane
Red Star possible starting lineup:
Popovic; Gobeljic, Milunovic, Degenek, Rodic; Jovancic, Canas; Garcia, Marin, Van la Parra; Pavkov
We say: Tottenham 2-0 Red Star Belgrade
It is getting to the stage where it feels as though it is generous to carry on predicting Tottenham wins. The hosts should come out on top in this one - they have superior quality and home advantage against a team with a woeful record on the road in Europe. However, with Spurs in their current form you can never truly tell, and it would not be the greatest surprise if Red Star manage to come away from North London with something.