With the country heading towards recession, Messi and his team-mates have the chance to spark some positive news for the papers to publish back home.
If successful they will bring the curtain down on one of the most glittering careers in football.
Switzerland's German coach Ottmar Hitzfeld announced before the tournament that it would be his final bow in the sport that has brought the 65-year-old among other titles two world coach of the year awards and two Champions League trophies.
The winners of the Argentina v Switzerland game will play whoever comes out on top in Tuesday's other match between Belgium - yet to lose a competitive match since Marc Wilmots took over the reins in 2012 - and the Jurgen Klinsmann-coached United States in Salvador.
The two victors will complete the quarter-finals line-up which on Monday saw European giants France and Germany become the latest two through as they eliminated Nigeria and Algeria to end African hopes of a World Cup title win.
The French will play the Germans on Friday in the Maracana, the first meeting of the two sides in a World Cup since the then West Germany beat Michel Platini-led France 2-0 in the 1986 semi-finals - four years after the epic last four clash which saw the Germans also prevail, this time on penalties, as the game finished 3-3 after extra-time.
More than 100,000 Argentine fans will flood Sao Paulo to see if Messi can work his magic again as he has done throughout the tournament so far.
Like Brazil's reliance on Messi's Barcelona team-mate Neymar, Argentina have got this far almost solely thanks to their captain's goals, scoring four of their six in the three group game victories.
Argentine coach Alejandro Sabella said he was happy for the two-time world champions to rely on him.
"I think both players are amazing. Messi's the best in the world, Neymar is a great player and of course with players like this the team depends on them. It's normal," he said.
Switzerland are calling Xherdan Shaqiri - who scored all the goals in the 3-0 triumph over Honduras - their own Messi. But Switzerland have never beaten Argentina at the World Cup in six previous attempts.
- Late Flight Home -
Belgium are waiting anxiously on the fitness of their talismanic captain and centre-back Vincent Kompany, who is struggling with a niggling groin injury.
However, Wilmots said even without Kompany the 'Red Devils' should go through to their first World Cup quarter-final since 1986 and if they slipped up he would consider it a "failure".
The 45-year-old former international striker - who is Belgium's all-time scorer at the finals with five in the three World Cups he played at - also batted away criticism of the unconvincing manner in which his side won their three group games.
"I let people make their complaints, we just advance. We are not going to bang our heads against the wall," he said.
"When I see the team giving everything, I have no regrets. We have a young team, unbeaten for a long time in competitive matches."
Klinsmann - who is bidding to guide the United States to their second ever appearance in the last eight emulating the 2002 side - is also brimming with confidence and has told his players to push their flights back to after the July 13 final.