In truth, the circumstances this time suggest such a pitiful outcome is unlikely. The Conmebol system is effectively rigged to ensure the big teams make it. And so tight is the scrap in the table behind the runaway leaders Brazil, that a couple of wins in their final three fixtures will transform things for Messi and his mates.
Especially as the reigning South American champions, Chile, who sit above Argentina on goal difference, are in the midst of a spectacular bout of self-destruction themselves.
Even so, a fearful sense of trepidation appears to have gripped the country. So jittery is the prevailing mood that even perpetual optimist Diego Maradona, a man keen to whip his shirt off and flourish it above his head at the merest hint of success, has voiced his disquiet.
The appointment in April of the excellent Sevilla manager Jorge Sampaoli, the third national coach of this campaign, temporarily lifted confidence after the desultory era of Edgardo Bauza. But last week's woeful, stodgy, goalless draw with Uruguay in his first game in charge has sunk everyone back into gloom.
Those wanting to know how collective fear and negativity can seep from the stands into the dressing room, could do worse than turn their attention to today's (NZ time) shenanigans in Buenos Aires. When it comes to voicing their concerns, fans in Argentina are not inclined to reticence.
Anything other than a resounding victory will provoke a backlash of unsuppressed fury. Another poor performance and the players might be advised to seek permanent asylum in Europe. For an entire golden generation to lose their gilding simultaneously indicates there is something wrong at the heart of the international set-up in Argentina.
Today (NZ time), things could get tasty, very tasty.
World Cup qualifying
• Only one thing is certain in South American World Cup qualifying: Brazil has advanced.
• The three other automatic berths are up for grabs with three rounds to play.
• Seven teams have a shot.
• The fifth-place team, currently Argentina, earns a match against New Zealand.
• Brazil leads the region with 36 points, followed by: Colombia (25), Uruguay (24), Chile (23), Argentina (23), Peru (21), Paraguay (21), Ecuador (20), Bolivia (10), Venezuela (7).
• In other matches today: Bolivia v Chile; Paraguay v Uruguay; and Ecuador v Peru.